Do Now 1/15/10 Copy HW in your planner. Copy HW in your planner. Text p. 462, #1-8 all, #10, #12,...

Do Now 1/15/10Do Now 1/15/10

Copy HW in your planner.Copy HW in your planner. Text p. 462, #1-8 all, #10, #12, #16-30 Text p. 462, #1-8 all, #10, #12, #16-30

evens, #36evens, #36

Be ready to finish quiz sections 7.1 – Be ready to finish quiz sections 7.1 – 7.4. You will have 10 minutes.7.4. You will have 10 minutes.

ObjectiveObjective

SWBAT identify the number of SWBAT identify the number of solutions of a linear systemsolutions of a linear system

““How Do You Solve a Linear How Do You Solve a Linear System???”System???”

(1) (1) Solve Linear Systems by Graphing (7.1)Solve Linear Systems by Graphing (7.1)

(2) (2) Solve Linear Systems by Substitution (7.2)Solve Linear Systems by Substitution (7.2)

(3) Solve Linear Systems by (3) Solve Linear Systems by ELIMINATION!!!ELIMINATION!!! (7.3)(7.3)

Adding or SubtractingAdding or Subtracting

(4) (4) Solve Linear Systems by Multiplying FirstSolve Linear Systems by Multiplying First (7.4) (7.4)

Then eliminate.Then eliminate.

Section 7.5 “Solve Special Types of Section 7.5 “Solve Special Types of Linear Systems”Linear Systems”

LINEAR SYSTEM-LINEAR SYSTEM-consists of two or more linear equations consists of two or more linear equations

in the same variables.in the same variables.

Types of solutions:Types of solutions:(1) (1) a a single pointsingle point of intersection of intersection – – intersecting linesintersecting lines

(2) (2) no solutionno solution – parallel lines – parallel lines

(3) (3) infinitely many solutionsinfinitely many solutions – when two – when two equations represent the same lineequations represent the same line

Equation 1 Equation 1

-3x + 2y = -9-3x + 2y = -9 Equation 2Equation 2

4x + 5y = 35 4x + 5y = 35

““Solve Linear Systems by Elimination” Solve Linear Systems by Elimination” Multiplying First!!” Multiplying First!!”

Equation 1 Equation 1 4x + 5y = 354x + 5y = 35 Substitute value forSubstitute value forx into either of the x into either of the original equations original equations 4(5) + 5y = 354(5) + 5y = 35

20 + 5y = 3520 + 5y = 35

The solution is the point (5,3). The solution is the point (5,3). Substitute (5,3) into both Substitute (5,3) into both

equations to check.equations to check.

4(5) + 5(3) = 354(5) + 5(3) = 3535 = 3535 = 35

-3(5) + 2(3) = -9-3(5) + 2(3) = -9-9 = -9-9 = -9

Multiply Multiply

FirstFirst

++ 23x = 11523x = 115

x = 5x = 5

y = 3y = 3

EliminatedEliminated

x (2)x (2)

15x - 10y = 4515x - 10y = 45 8x + 10y = 70 8x + 10y = 70

x (-5)x (-5)

““Consistent IndependentConsistent IndependentSystem”System”

3x + 2y = 2 3x + 2y = 2 Equation 2Equation 2

3x + 2y = 10 3x + 2y = 10

““Solve Linear Systems with No Solve Linear Systems with No Solution”Solution”

0 = 80 = 8

No SolutionNo Solution

EliminatedEliminated EliminatedEliminated

-3x + (-2y) = -2 -3x + (-2y) = -2 +This is a false statement,therefore the system has nosolution.

By looking at the graph, the lines are PARALLEL and therefore willnever intersect.

“ “InconsistentInconsistentSystem”System”

Equation 2Equation 2

x – 2y = -4 x – 2y = -4

““Solve Linear Systems with Infinitely Many Solve Linear Systems with Infinitely Many Solutions”Solutions”

-4 = -4-4 = -4

Infinitely Many SolutionsInfinitely Many Solutions

y = ½x + 2 y = ½x + 2

This is a true statement,therefore the system has infinitely many solutions.

By looking at the By looking at the graph, the lines are the graph, the lines are the SAME and therefore SAME and therefore intersect at every point, intersect at every point, INFINITELY!INFINITELY!

“ “ConsistentConsistentDependentDependent

System”System”

Equation 1 Equation 1 x – 2y = -4x – 2y = -4

Use ‘Substitution’ Use ‘Substitution’ because we know because we know what y is equals.what y is equals.

x – x – 4 = -4x – x – 4 = -4 x – x – 22(½x + 2)(½x + 2) = -4 = -4

5x + 3y = 6 5x + 3y = 6

““Tell Whether the System has NTell Whether the System has No o SolutionsSolutions or or Infinitely Many Infinitely Many

SolutionsSolutions””

0 = 90 = 9

No SolutionNo Solution

EliminatedEliminated EliminatedEliminated

-5x - 3y = 3 -5x - 3y = 3 This is a false statement,therefore the system has nosolution.

“ “InconsistentInconsistentSystem”System”

-6x + 3y = -12 -6x + 3y = -12

-12 = -12-12 = -12

Infinitely Many SolutionsInfinitely Many Solutions

y = 2x – 4 y = 2x – 4

This is a true statement,therefore the system has infinitely many solutions.

“ “ConsistentConsistentDependentDependent

System”System”

Equation 1 Equation 1 -6x + 3y = -12-6x + 3y = -12

Use ‘Substitution’ Use ‘Substitution’ because we know because we know what y is equals.what y is equals.

-6x + 6x – 12 = -12-6x + 6x – 12 = -12 -6x + 3-6x + 3(2x – 4)(2x – 4) = -12 = -12

““Tell Whether the System has NTell Whether the System has No o SolutionsSolutions or or Infinitely Many Infinitely Many

SolutionsSolutions””

How Do You Determine the How Do You Determine the Number of Solutions of a Number of Solutions of a

Linear System?Linear System?

Number of Number of SolutionsSolutions

Slopes and y-Slopes and y-interceptsintercepts

One solutionOne solution Different slopesDifferent slopes

No solutionNo solution Same slope Same slope

Different y-interceptsDifferent y-intercepts

Infinitely many Infinitely many solutionssolutions

Same slope Same slope

Same y-interceptSame y-intercept

(1)First rewrite the equations in slope-intercept form. (2)Then compare the slope and y-intercepts.

y = mx + by = mx + bslope y -intercept

““Identify the Number of Identify the Number of Solutions”Solutions”

Without solving the linear system, Without solving the linear system, tell whether the system has tell whether the system has one one solution, no solution, solution, no solution, or or infinitely infinitely many solutions.many solutions. 5x + y = -25x + y = -2

-10x – 2y = 4-10x – 2y = 46x + 2y = 36x + 2y = 3

6x + 2y = -56x + 2y = -5

Infinitely many Infinitely many solutionssolutions

No solutionNo solution

3x + y = -93x + y = -9

3x + 6y = -123x + 6y = -12

One solutionOne solution

y = -5x – 2y = -5x – 2

– – 2y =10x + 42y =10x + 4

y = -5x – 2y = -5x – 2

y = 3x + 3/2 y = 3x + 3/2

y = 3x – 5/2y = 3x – 5/2y = -3x – 9y = -3x – 9

y = -½x – 2 y = -½x – 2

WAR!!WAR!!“Identify the Number of “Identify the Number of

Solutions”Solutions” Without solving the linear system, Without solving the linear system,

tell whether the system has tell whether the system has one one solution, no solution, solution, no solution, or or infinitely infinitely many solutions.many solutions.

HomeworkHomework

Text p. 462, #1-8 all, #10, #12, #16-30 Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36evens, #36

NJASK7 PrepNJASK7 Prep

Do Now 1/15/10 Copy HW in your planner. Copy HW in your planner. Text p. 462, #1-8 all, #10, #12,...

Documents

Transcript of Do Now 1/15/10 Copy HW in your planner. Copy HW in your planner. Text p. 462, #1-8 all, #10, #12,...

Do Now 12/7/09 Take out HW from last night. Take out HW from last night. –Text page 190, #16-36 evens Copy HW in your planner. Copy HW in your planner.

Do Now 4/1/13 Copy HW in your planner. Copy HW in your planner. Text p. 312, #1-16 all, 21 Be ready to copy POTW #2 Be ready to copy POTW #2.

Do Now 1/10/11 Copy HW in your planner. Copy HW in your planner. Text p. 430, #4-20 evens, 30-34 evens Text p. 430, #4-20 evens, 30-34 evens Text p. 439,

· 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 462 003 357, 462 003 462 038 462 002 309, 52 g 462 011 107 462 042 20 a, 2, 462 011 462 013 462 023 (0755) 2660088

Do Now 1/30/12 Copy HW in your planner. Copy HW in your planner. Text p. 278, #1-13 all, #20 & 21 Text p. 278, #1-13 all, #20 & 21 In your notebook, put.

Do Now 4/12/10 Copy HW in your planner. Copy HW in your planner. Text p. 632, #3-5, 12 – 32 multiples of 4, #40 Text p. 632, #3-5, 12 – 32 multiples of.

Do Now 1/26/10 Copy HW in your planner. Copy HW in your planner. –Benchmark Test 4 review worksheet…

Do Now 5/4/10 Take out HW from last night. Take out HW from last night. Cumulative Test Chapters 1-10 Cumulative Test Chapters 1-10 Copy HW in your planner.

Do Now 1/11/10 Copy HW in your planner. Copy HW in your planner. Text p. 430, #4-20 evens, 30-34 evens Text p. 430, #4-20 evens, 30-34 evens Text p. 439,

Do Now 2/8/10 Copy HW in your planner. Copy HW in your planner. Text p. Text p. 272, #10-36 evens, #44, & #47 Be ready to copy POTW #2 Be ready to.

Do Now 3/8/11 Take out HW from last night. Take out HW from last night. Text p. 228, #10-28 evens, 38-44 evens Copy HW in your planner. Copy HW in your.

Do Now 10/22/13 Copy HW in your planner. Copy HW in your planner. Text p. 74, #1-3, 8-13, 38, 39, & 41 Text p. 74, #1-3, 8-13, 38, 39, & 41 In your journal,

Do Now 1/31/11 Take out HW from Tuesday night. Take out HW from Tuesday night. –“The Sieve of Eratosthenes” Copy HW in your planner. Copy HW in your planner.

Do Now 1/24/12 Copy HW in your planner. Copy HW in your planner. –Mid-Term Review worksheet #1 Take out Benchmark Tests #1-4. Take out Benchmark Tests.

Learning Target HW in Planner · HW in Planner: Math Journal- p.162 Due: Tues., 2/16 Test Corrections It's like extra credit and the fastest way to bring up your grade. If you need

Do Now 4/2/13 Take out HW from last night. Take out HW from last night. Text p. 312, #1-16 all, 21 Text p. 312, #1-16 all, 21 Copy HW in your planner.

Take out HW from last night. Take out HW from last night. Text p. 379, #1-6 Text p. 379, #1-6 Copy HW in your planner. Copy HW in your planner. Text p.

Do Now 1/24/11 Copy HW in your planner. Copy HW in your planner. –Mid-Term Review worksheet #2, #1-13 Take out Benchmark Tests #1-4. Take out Benchmark.

Take out HW from last night. Take out HW from last night. Text p. 376, #1-24 all Text p. 376, #1-24 all Copy HW in your planner. Copy HW in your planner.

Do Now 2/21/12 Take out HW from last night. Take out HW from last night. Text p. 248, #7-16, 19 & 20 Text p. 248, #7-16, 19 & 20 Copy HW in your planner.