1. Solve a system of linear equation in two variables
The Substitution Method
Solve the system using the graphing method:
y = x + 9
x + y = 0
Solution: (-1, 3)

2. Solve a system of linear equation in two variables
The Substitution Method
x + y = 15
4x + 3y = 38
To solve a system using the substitution method:
1. Solve one of the equations for one of the variables.
x + y = ⇨ x = 15 – y
2. Substitute this expression into the other equation.
4x + 3y = ⇨ 4(15 – y) + 3y = 38
3. Solve the resulting equation.
4(15 – y) + 3y = 38
60 – 4y + 3y = 38
60 – y = 38
-y = -22
y = 22

3. Solve a system of linear equation in two variables
The Substitution Method
x + y = 15
4x + 3y = 38
4. Use your answer from step 3 to substitute into your equation in step 1 and solve.
x + y = 15
x+22 = 15
x = -7
Solution: (-7, 22)
5. Check your solution in both equations.
x + y = x + 3y = 38
= (-7) + 3(22) = 38
15 = 15 ⋆ = 38
38 = 38 ⋆

4. Solve a system of linear equation in two variables
The Substitution Method
To solve a system using the substitution method:
1. Solve for one of the variables
2. Substitute into the other equation.
3. Solve the resulting equation.
4. Substitute this answer into the equation.
5. Check.

5. Solve a system of linear equation in two variables
The Substitution Method
Solve the system using the Substitution Method.
y = 2x
5x – y = 30
2. 2x – y = 17
3x + 4y = -13
5x – (2x) = 30
-y = -2x + 17
y = 2x - 17
3x = 30
x = 10
3x + 4(2x – 17) = -13
3x + 8x – 68 = -13
11x = 55
x = 5
y = 2(10)
y = 20
y = 2(5) – 17
y = 10 – 17
y = -7
Solution: (10, 20)
Solution: (5, -7)

6. Solve a system of linear equation in two variables
The Substitution Method
Solve the system using the Substitution Method.
3. 3x + 1 = y
2x + 3y = 25
4. 5y – 2x = 3
6x = 15y - 1
5. 3y – 6x = 24
8 + 2x = y