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Elimination Method for solving Linear Systems Step 1: Step 2: Step 3: Step 4: Name: Find or Make Opposites (coefficients for x or y) Add the equations and solve for the remaining letter. Plug your answer into either of the original equations. Write your answer as an ordered pair and check. Example: 3x + 5y = 13 I don’t see opposites, so I decide to make 3x and 2x opposites… 2x + 7y = 16 I multiply the entire top row by 2 and the bottom by -3… one of them has to be negative, but it doesn’t matter which one 6x + 10y = 26 Don’t forget to multiply the 13 and 16 as well. -6x – 21y = -48 Now I have 6x and -6x, so I can add to cancel. 0 – 11y = -22 Drop the zero -11y = -22 Divide by -11 y=2 3x + 5(2) = 13 3x + 10 = 13 3x = 3 x=1 Answer (1, 2) 1. 3x – 2y = 8 -3x + 3y = -3 2. 2x – 4y = 4 -3x + 4y = -8 3. 2x + 5y = -1 -2x – 3y = 3 4. 2x + 5y = -14 -3x – 5y = 11 Plug your answer into either equation, I chose the top one. subtract 10 from both sides. divide by 3 on both sides write your answer as an ordered pair. 5. 2x – 3y = 8 -4x + 5y = -10 6. 3x – 6y = 3 -4x + 3y = -9 7. 9x – 2y = 21 -3x + 5y = 6 8. 6x + 6y = -12 -5x – 2y = 22 9. 4x + 5y = 2 -6x - 2y = -14 10. 7x + 6y = -12 -4x – 9y = -21