# Solving a System of Equations by SUBSTITUTION. GOAL: I want to find what x equals, and what y equals. Using substitution, I can say that x = __ and y.

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Solving a System of Equations by SUBSTITUTION

GOAL: I want to find what x equals, and what y equals. Using substitution, I can say that x = __ and y =__; then I can make my ordered pair (x, y) - which is my solution.

Set Up Your Paper: Equation x = ____(, ) Equation y = ____

1.Solve original expression 1.Solve the first equation (original) for one variable (unless already done) = expression y = 2x 2. Substitute expression other variable (1 st solution) 2. Substitute the expression into the 2 nd equation and solve for the other variable (1 st solution) 2x = 12 – x x = 4 original 2 nd equation 4 4

3. Substitute 1 st solution original 3. Substitute the 1 st solution back into original equation y = 2(4) 4. Solve 4. Solve for 2 nd variable y = 8 5. 5. Check the solution 8 = 2(4) 8 = 8 4 4 8 8

3x + y = -8 x = ___ (, ) 8x + 2y = -12 y = ___ 1.Solve original expression 1.Solve the first equation (original) for one variable (unless already done) = expression y = -3x - 8 2. Substitute expression other variable (1 st solution) 2. Substitute the expression into the 2 nd equation and solve for the other variable (1 st solution) 8x + 2(-3x – 8) = -12 x = 2 original 2 nd Equation 22

3. Substitute 1 st solution original 3. Substitute the 1 st solution back into original equation -3(2) + y = -8 4. Solve 2 nd variable 4. Solve for 2 nd variable y = -2 5. 5. Check the solution -3(2) + (-2) = -8 -8 = -8 -3x + y = -8 x = 2 (2, -17 ) 8x + 2y = -12 y = ___ -2

y = x + 1 y = 2x - 1

y = -2x + 3 y = 5x - 4

Review What are the steps for solving a system of equations by substitution?

Steps : 1. Solve original expression 1. Solve the first equation (original) for one variable (unless already done) = expression 2. Substitute expression other variable (1 st solution) 2. Substitute the expression into the 2 nd equation and solve for the other variable (1 st solution) 3. Substitute 1 st solution original 3. Substitute the 1 st solution back into original equation 4. Solve 4. Solve for 2 nd variable 5. 5. Check the solution

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