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Solving Linear Systems: Graphing, Substitution, Combination

Learn how to solve linear systems using graphing, substitution, and combination methods with step-by-step examples and explanations. Practice solving systems of equations and find ordered pair solutions.

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Solving Linear Systems: Graphing, Substitution, Combination

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  1. Table of Contents Topic Page # ... 7.1 Solve Systems By Graphing 76 7.2 Solve Systems By Substitution 77 7.3 Solve Systems By Combination 78 7.4 Multiplication w/ Combination 79

  2. Solve Systems by Substitution: • Line up the x and y values in standard form • Make one variable opposite each other if needed by multiplying • Add the equations • Solve for the variable • Plug answer into any equation to find the other variable • Write answer as ordered pair (x,y)

  3. Ex #1: Solve the linear system using elimination. 7x – 2y = 5 a. + (–1) -7x + 3y = -4 y = 1 7x – 2(1) = 5 7x = 7 x = 1 (1, 1) ans:_______________

  4. 4x + 3y = 2 b. + (–1) -5x – 3y = 2 -x = 4 x = -4 4(-4) + 3y = 2 -16 + 3y = 2 3y = 18 y = 6 (-4, 6) ans:_______________

  5. 4x + y = -10 c. + (–1) -2x – y = 14 2x = 4 x = 2 4(2) + y = -10 8 + y = -10 y = -18 (2, -18) ans:_______________

  6. x – y = -4 d. + -x – 3y = -4 (–1) -4y = -8 y = 2 x – 2 = -4 x = -2 (-2, 2) ans:_______________

  7. Solving Linear Systems by Multiplying First 6x – 2y = 1 + -6x + 9y = -15 (3) 7y = -14 y = -2 6x – 2(-2) = 1 6x + 4 = 1 6x = -3 x = -½ (-½, -2) ans:_______________

  8. a. 10x + 4y = 32 (2) + 3x – 4y = 20 13x = 52 x = 4 10(4) + 4y = 32 40 + 4y = 32 4y = -8 y = -2 (4, -2) ans:_______________

  9. b. 6x + 5y = 19 + -6x – 9y = -15 (-3) -4y = 4 y = -1 6x + 5(-1) = 19 6x – 5 = 19 6x = 24 x = 4 (4, -1) ans:_______________

  10. c. 12x + 15y = 105 (3) + -12x + 8y = -36 (4) 23y = 69 y = 3 -12x + 8(3) = -36 -12x + 24 = -36 -12x = -60 x = 5 (5, 3) ans:_______________

  11. d. 35x + 15y = -60 (5) + -6x – 15y = -114 (-3) 29x = -174 x = -6 35(-6) + 15y = -60 -210 + 15y = -60 15y = 150 y = 10 (-6, 10) ans:_______________

  12. Systems Project Tape System In Name: _________ Blk: ___________

  13. Solve for y • Make a b/m chart • Graph both equations • Intersection is answer Pg.1

  14. Solve System by Graphing Write Your System Here y = y = ans:__________ Tape Graph Here Pg.2

  15. Solve for a variable • Plug into other equation • Solve • Plug into 1st equation • Write answer as (x, y) Pg.3

  16. Solve System by Substitution Write Your System Here ans:__________ Pg.4

  17. Line up the x and y • Get variable to be opposite by multiplying • Add equations • Solve • Plug back into any equation • Write answer as (x, y) Pg.5

  18. Solve System by Elimination Write Your System Here ans:__________ Pg.6

  19. Best Method Pg.7

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