1 / 24

Let ’ s Warm Up!

Let ’ s Warm Up!. 1) Solve the system of equations by graphing: 2x + 3y = 12 2x – y = 4 Answer: 2) Find the slope-intercept form for the equation of a line that passes through (0, 5) and is parallel to a line whose equation is 4x – y = 3? Answer: 3)Solve 3│x – 5│= 12 Answer:.

mary-battle
Télécharger la présentation

Let ’ s Warm Up!

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Let’s Warm Up! 1) Solve the system of equations by graphing: 2x + 3y = 12 2x – y = 4 Answer: 2) Find the slope-intercept form for the equation of a line that passes through (0, 5) and is parallel to a line whose equation is 4x – y = 3? Answer: 3)Solve 3│x – 5│= 12 Answer: (3, 2) y=4x+5 x= 1, 9

  2. Let’s chat about finals • Wednesday Jan 22nd : 2, 4, 6 • Thursday Jan 23rd : 1, 3, 5 • Minimum Days • Final Review sheet • due DAY OF FINAL

  3. Mini Quiz Time! • 3 graphing Questions • Get out a pencil please.

  4. 8-2 Substitution Objective: To use the substitution method to solve systems of equations.

  5. Two Algebraic Methods: • Substitution Method • Elimination Method  will learn about next 

  6. RECALL…Three Types of Solutions: Intersection is Solution Infinite Solutions One Solution No Solution Same slope Same y-intercept “Same line  Intersect infinitely” Different slope Different y-intercept “Intersect at one point” Same slope Different y-intercept “Run parallel  Never intersect”

  7. Substitution Method • Use the substitution method when: • one equation is set equal to a variable • y = 2x + 1 or x = 3y - 2

  8. Example 1 • Instead of x = 2 we have: x = y + 2 x + 2y = 11 (y + 2) + 2y = 11 3y + 2 = 11 3y = 9 y = 3 These are all the same! x = 3 + 2 x = 5 Answer: (5,3)

  9. Try with a Mathlete • y = 3x x + 2y = -21 • y = 2x – 6 3x + 2y = 9 Answers: 1) (-3,-9) 2) (3,0)

  10. Example 2 x + 4y = 1 2x – 3y = -9 • First, solve for a variable x = -4y + 1 2(-4y + 1) – 3y = -9 -8y + 2 – 3y = -9 -11y + 2 = -9 -11y = -11 y = 1 Solve for x (because there is no number in front of it) x = -4(1) + 1 x = -3 Answer: (-3,1)

  11. TOO • 2y = -3x 2) 2x – y = -4 4x + y = 5 -3x + y = -9 Answers: 1) (2,-3) 2) (13,30)

  12. x + y = 16x = 16 – y 2y = -2x + 2 2y = -2(16 – y) + 2 2y = -32 + 2y + 2 2y = -30 + 2y 0 = -30 False NO SOLUTION 6x – 2y = -4 y = 3x + 2 6x – 2(3x + 2) = -4 6x – 6x – 4 = -4 -4 = -4 True INFINITELY MANY Special Cases

  13. TOO for Homework 1) y = -x + 3, 2y + 2x = 4 2) x + y = 0, 3x + y = -8 3) y = 3x – 7, 3x – y = 7

  14. Homework Pg. 467 #17-32 left column

  15. Pg. 467 #17-32 Left ColumnSolve using substitution. 17. 26. 20. 29. 23. 32.

  16. MORE Explanations The following slides have more examples and explanations of the substitution method.

  17. Examples: Use the substitution method to solve the system of equations. (use the substitution method when a variable is already isolated or when a variable has a coefficient of 1 and can easily be transformed) 1) 2x + 3y = 2 x – 3y = –17 1st: Transform one equation to isolate a variable 2nd: Substitute into the other equation and solve for variable #1 3rd: Substitute into transformed equation from 1st step and solve for variable #2 2x + 3y = 2 “x = 3y – 17” 2(3y – 17) + 3y = 2 6y – 34 + 3y = 2 –34 + 9y = 2 +34 +34 9y = 36 9 9 y = 4 x = 3y – 17 “y = 4” x = 3(4) – 17 x = 12 – 17 x = –5 x – 3y = –17 +3y +3y x = 3y – 17 (we picked x – 3y = – 17 because x has a coefficient of 1 and can easily be transformed) One Solution (–5 , 4) Write answer as an ordered pair (x, y):

  18. Examples: Use the substitution method to solve the system of equations. (use the substitution method when a variable is already isolated or when a variable has a coefficient of 1 and can easily be transformed) 2) –9x + 3y = –21 3x – y = 7 1st: Transform one equation to isolate a variable 2nd: Substitute it into the other equation and solve for variable #1 3rd: Substitute into the transformed equation from 1st step and solve for variable #2 –9x + 3y = –21 “y = 3x – 7” –9x + 3(3x – 7) = –21 –9x + 9x – 21= –21 –21 = –21 3x – y = 7 -3x -3x –y = –3x + 7 -1 -1 -1 y = 3x – 7 True!! (we picked 3x – y = 7 because y has a coefficient of -1 and can easily be transformed) Infinite Solutions Write answer as an ordered pair (x, y):

  19. Examples: Use the substitution method to solve the system of equations. (use the substitution method when a variable is already isolated or when a variable has a coefficient of 1 and can easily be transformed) 3) 4x – 2y = 5 y = 2x + 1 1st: Transform one equation to isolate a variable 2nd: Substitute into the other equation and solve for variable #1 3rd: Substitute into transformed equation from 1st step and solve for variable #2 4x – 2y = 5 “y = 2x + 1” 4x – 2(2x + 1) = 5 4x – 4x – 2 = 5 – 2 = 5 y = 2x + 1 (already isolated) False!! No Solution

  20. Chapter 8 Systems of Equations 8-2 Substitution We will become experts at solving systems of equations with substitution.

  21. Math Lab • Solve the system with substitution: x = y + 2 x + 2y = 11 (y + 2) + 2y = 11 3y + 2 = 11 3y = 9 y = 3 These are all the same! x = 3 + 2 x = 5 Answer: (5,3)

  22. Math Lab ReviewSubstitution • y = -x + 3 2y + 2x = 4 y = 3x – 7 3x – y = 7 x + y = 0 3x + y = -8

  23. x + y = 16x = 16 – y 2y = -2x + 2 2y = -2(16 – y) + 2 2y = -32 + 2y + 2 2y = -30 + 2y 0 = -30 False NO SOLUTION 6x – 2y = -4 y = 3x + 2 6x – 2(3x + 2) = -4 6x – 6x – 4 = -4 -4 = -4 True INFINITELY MANY Special Cases

  24. Partner Big Yellow Dice Game

More Related