1. Solving Systems of Equations by Substitution
Teacher Twins©2014

2. Warm Up
(8, -2)
(3, 9)
No solution
(4, 6)

3. Solving Systems of Equations by Substitution

4. 4x-y=-4 4x-2x=-4 2x=-4 x = -2 Example 1
Solve the system by substitution.
y=2x
4x-y=-4
Substitute 2x for y in the second equation.
4x-y=-4
4x-2x=-4
2x replaces the y because y = 2x
2x=-4
x = -2
Combine like terms and solve

5. Use y = 2x to find the value of y .
Solve
y=-4
The solution is (-2,-4).

6. Example 2 x=2y -x + y=-2 Substitute 2y for x in the second equation.
Solve the system by substitution.
x=2y
-x + y=-2
Substitute 2y for x in the second equation.
Notice when I substitute I have the same variable so I can solve the equation.
-(2y) + y = -2
-y = -2
y = 2
Combine like terms and solve

7. Use x = 2y to find the value of x .
The solution is (4, 2).

8. Ex 3: Solve the system by substitution.
-3x + 3y = 4
-x + y = 3
y = x + 3
-3x + 3( x + 3) = 4
-3x + 3x + 9 = 4
9 = 4 is not true.
The solution is no solution.

9. Ex 4: Solve the system by substitution.
-3x + 3y = 12
-x + y = 4
y = x + 4
-3x + 3( x + 4) = 12
-3x + 3x + 12 = 12
12 = 12 is true.
The solution is infinitely many solutions.

10. Practice
Solve each system by substitution.
2x – 3y = -1
y = x – 1
2. 6x + 6y = - 6
5x + y = -13
The solution is (4, 3).
The solution is (-3, 2).

11. Closure
Explain why this method for solving systems of equations is called substitution.