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 = ____

y = 2x x = ___ ( , )

y = 12 – x y = ___

1. Solve the first equation (original) for one variable (unless already done) = expression

y = 2x2. Substitute the expression into the 2nd equation and solve for the other variable (1st solution)

2x = 12 – xx = 4

original

2nd equation

4 4

3. Substitute the 1st solution back into original equation

y = 2(4)4. Solve for 2nd variable

y = 85. Check the solution

8 = 2(4)8 = 8

y = 2x x = ___ ( , )

y = 12 – x y = ___

4 48

8

3x + y = -8 x = ___ ( , )

8x + 2y = -12 y = ___

1. Solve the first equation (original) for one variable (unless already done) = expression

y = -3x - 8

2. Substitute the expression into the 2nd equation and solve for the other variable (1st solution)

8x + 2(-3x – 8) = -12x = 2

original

2nd Equation

22

3. Substitute the 1st solution back into original equation

-3(2) + y = -8

4. Solve for 2nd variabley = -2

5. Check the solution-3(2) + (-2) = -8-8 = -8

-3x + y = -8 x = 2 (2, -17 )

8x + 2y = -12 y = ___-2

y = x + 1y = 2x - 1

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

Review

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

Steps :1. Solve the first equation (original) for one

variable (unless already done) = expression2. Substitute the expression into the 2nd equation

and solve for the other variable (1st solution)3. Substitute the 1st solution back into original

equation 4. Solve for 2nd variable5. Check the solution