Transcript

A2 9.2Determine whether each function represents growth or
decay.

1. () = &' ( ) * 2. () = +

5. () = &+ , ) * 6. () = −&+

' &+ , ) *

Depreciation: You buy a new computer and accessories for $1200. The value of the computer decreases by 30% each year. 11. Write an exponential decay model giving the computer’s value V (in dollars) after t years. 12. What is the value of the computer after 4 years?

Graph each equation. 13. () = &,

' ) * 14. () = 2 • &+

' ) * + 2

D: R: D: R: 17. () = (0.5)*8+ 18. () = &+

, ) *9,

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

1. () = &' ( ) * 2. () = +

5. () = &+ , ) * 6. () = −&+

' &+ , ) *

Depreciation: You buy a new computer and accessories for $1200. The value of the computer decreases by 30% each year. 11. Write an exponential decay model giving the computer’s value V (in dollars) after t years. 12. What is the value of the computer after 4 years?

Graph each equation. 13. () = &,

' ) * 14. () = 2 • &+

' ) * + 2

D: R: D: R: 17. () = (0.5)*8+ 18. () = &+

, ) *9,

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name______________________

Systems Unit Review Graph the system of equations and determine the solution.

1. x + 2y = 7 3x + y = 6 ! " #

2. x − 5y = −5 3x −15y = 9 " # $

3. x + y = 4 2x − y = 6 " # $

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

4. 6x −3y =12 −2x + y = −4 " # $

5. x + 2y =11 4x +3y = 9 ! " #

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

y = x 1

10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

( 0.5x 0.3y = 1.3

1.4x+ 1.2y = 2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

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