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Page 1: Assignment 9.2: Graphing Exponential Decay

Algebra 2 Name______________________________ ALT 09

Assignment 9.2: Graphing Exponential Decay

Determine whether each function represents growth or decay.

1. 𝑓(𝑥) = &'()* 2. 𝑓(𝑥) = +

,(3*) 3. 𝑓(𝑥) = &.

')* 4. 𝑓(𝑥) = (0.8)*

Match the function with its graph.

5. 𝑓(𝑥) = &+,)* 6. 𝑓(𝑥) = −&+

,)* 7. 𝑓(𝑥) = 3 &+

,)*

8. 𝑓(𝑥) = +

'&+,)* 9. 𝑓(𝑥) = −3 &+

,)* 10. 𝑓(𝑥) = −+

'&+,)*

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?

Page 2: Assignment 9.2: Graphing Exponential Decay

Graph each equation. 13. 𝑓(𝑥) = &,

')* 14. 𝑓(𝑥) = 2 • &+

,)*

D: R: D: R: 15. 𝑓(𝑥) = −(0.25)* 16. 𝑓(𝑥) = &+

')*+ 2

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

,)*9,

− 1 D: R: D: R:

Algebra 2 Name______________________

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

1. x + 2y = 73x + y = 6!"#

2. x − 5y = −53x −15y = 9"#$

3. x + y = 42x − 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 =114x +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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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 = 73x + y = 6!"#

2. x − 5y = −53x −15y = 9"#$

3. x + y = 42x − 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 =114x +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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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 = 73x + y = 6!"#

2. x − 5y = −53x −15y = 9"#$

3. x + y = 42x − 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 =114x +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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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 = 73x + y = 6!"#

2. x − 5y = −53x −15y = 9"#$

3. x + y = 42x − 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 =114x +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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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 = 73x + y = 6!"#

2. x − 5y = −53x −15y = 9"#$

3. x + y = 42x − 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 =114x +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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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 = 73x + y = 6!"#

2. x − 5y = −53x −15y = 9"#$

3. x + y = 42x − 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 =114x +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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

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

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(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.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

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