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Name: Period: Elimination Using Multiplication Study Guide Some systems of equations cannot be solved simply by adding or subtracting the equations. A number must first multiply one or both equations before the system can be solved by elimination. Consider the following example. Example: Use elimination to solve the system of equations x + 2y = 2 and 4x +5y = 5 x + 2y = 2 4x +5y = 5 Multiply –4(x + 2y = 2) Then add the equations. -4x – 8y = -8 4x +5y = 5 -3y = -3 y=1 Substitute 1 for y into either equation and solve for x. x + 2(1) = 2 x+2=2 x=0 The solution of the system is (0, 1). Use elimination to solve each system of equations. 1. 3x + 2y = 0 x – 5y = 17 2. 2x + 3y = 6 x + 2y = 5 3. 3x – y = 2 x + 2y = 3 4. 2x + 5y = 3 -x + 3y = -7 5. 2x + y = 3 -4x – 4y = -8 6. 5x – 2y = -10 3x + 6y = 66 Name: Period: Use elimination to solve each system of equations. 7. 7x + 4y = -4 5x + 8y = 28 8. 4x – 2y = -14 3x – y = -8 9. 5x + 3y = -10 3x + 5y = -6 10. 2x + y = 0 5x + 3y = 2 Substitution Review: Use the substitution method to solve each system of equations. 11. y = 4x x+y=5 12. x = -4y 3x + 2y = 20 13. y = x – 1 x+y=3 14. 3x – y = 4 2x – 3y = -9 15. 2x + 3y = 7 3x – y = 5 16. x + 6y = 2 2x + 2y = -1