1. Goal: Solve systems of linear equations using elimination. Eligible Content: A1.1.2.2.1 / A1.1.2.2.2

2.  Elimination Method – the process of adding two equations together to get a variable to cancel out.  Also called the Linear Combinations Method.  Opposites – two numbers that are the same distance from 0.

3. 1. Multiply one or both equations by any numbers that will give you opposite coefficients for a variable. 2. Add the two equations together and solve for the remaining variable. 3. Plug your answer from Step 2 into any equation to solve for the other variable. 4. Write your answer as an ordered pair. 5. Check your answer.

4. 2x + 5y = 5 3x + 2y = -9 2x + 5y = 5 2x + 5 * 3 = 5 2x + 15 = 5 - 15 -15 2x = -10 2 2 x = -5 6x + 15y = 15 -6x – 4y = 18 11y = 33 11 11 y = 3 (-5, 3) 3 ( ) -2( )

5. What would you multiply by for each problem?  2x + 3y = 9 and 4x + 4y = 10  -5x – 2y = 10 and 3x + 7y = 12  2x + y = 5 and 3x – 4y = 14  18x + 12y = 90 and 12x + 8y = 72

6. 1. 4x + 3y = 16 2x – 3y = 8 (4, 0) 2. -2x + 3y = 12 2x – 8y = -52 (6, 8) 3. 3x + 5y = 6 -4x + 2y = 5 (-0.5, 1.5) 4. 2x + 3y = 0 5x – 6y = 27 (3, -2) 5. -7x + 9y = 3 6x – 4y = 16 (6, 5)

7. Use elimination to solve the system of equations. 3x – 5y = 1 2x + 5y = 9 A.(1, 2) B.(2, 1) C.(0, 0) D.(2, 2)

8. Use elimination to solve the system of equations. 9x – 2y = 30 x – 2y = 14 A.(2, 2) B.(–6, –6) C.(–6, 2) D.(2, –6)

9. Use elimination to solve the system of equations. x + 7y = 12 3x – 5y = 10 A.(1, 5) B.(5, 1) C.(5, 5) D.(1, 1)

10. A.(–4, 1) B.(–1, 4) C.(4, –1) D.(–4, –1) Use elimination to solve the system of equations. 3x + 2y = 10 2x + 5y = 3

11. 1. x + 3y = 5 2x – 3y = 1 2. 4x – 3y = 0 2x + 4y = -22 3. 5x + 7y = 31 2x + 3y = 12 (2, 1) (-3, -4) (9, -2)

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