1. Notes 6.5, Date__________ (Substitution)

2. To solve using Substitution: 1.Solve one equation for one variable (choose the variable with a coefficient of one) 2.Substitute this expression into your other equation 3.Solve for the variable 4.Substitute this value back into the equation from step 1. 5.Solve for the other variable y = 3x + 52x + 3y = 37 2x + 3(3x + 5) = 37

3. Solve the System x + y = -40 y = 4x x + (4x) = -40 substitute 5x = -40 5 x = -8 solve

4. Solve the System x + y = -40 y = 4x x = -8 Substitute for x to find y y = 4(-8) y = -32 or (-8) + y = -40 +8 y = -32 (-8,-32)

5. Solve the System 2x + y = 7 x -2y = 1 2(2y + 1) + y = 7 substitute 4y + 2 + y = 7 y = 1  x = 2y + 1 5y + 2 = 7 5y = 5 solve

6. Solve the System 2x + y = 7 x = 2y + 1 y = 1 Substitute for y to find x x = 2(1) + 1 x = 3 2x + (1) = 7 2x = 6 x = 3 or ( 3,1 )

7. Solve the System y = -2x + 11 y = -34 + 7x -2x + 11 = -34 + 7x substitute +2x 9 11 = -34 + 9x +34 45 = 9x x = 5 solve

8. Solve the System y = -2x + 11 y = -34 + 7x x = 5 Substitute for x to find y y = -2(5) + 11 y = -10 + 11 y = 1 (5,1)