1. 8.2 Solving by Substitution
Objective: To solve a system of equations by substituting for a variable

2. Solving by Substitution
When one variable is alone on one side of the equation, you can substitute for that variable in the other equation.
x + y = 13
x = y + 3
(y + 3) + y = 13
x = 5 + 3
2y + 3 = 13
x = 8 -3
2y = 10
(8, 5)
y = 5

3. Solving by Substitution
y = 3x 3x
2x + 4y = 28
y = 3( )
2x + 4( ) = 28
2x + 12x = 28
y = 6
14x = 28
(2, 6)
x = 2 2

4. Solving by Substitution
(3, 2)
x + y = 5
x = y + 1
(y + 1) + y = 5
x = 2 + 1
2y + 1 = 5
x = 3 -1
2y = 4
y = 2

5. Solving by Substitution
(1, 7)
x + y = 8
y = 2 + 5x
x + (2 + 5x)= 8
y = 2 + 5(1)
6x + 2 = 8
y = 7 -2
6x = 6
x = 1

6. Solving by Substitution
y = x + 2 3
y = 2x - 1
y = 5
x + 2 = 2x - 1 -x
2 = x - 1
(3, 5)
3 = x

7. Solve for X
Solve for y

8. Solving by Substitution
(4, 1)
x + y = 5
2x + 3y = 11 -y
Parenthesis!!!
x = 5 - y 1
2(5 – y) + 3y = 11
x = 4
10 – 2y + 3y = 11
10 + y = 11
y = 1

9. Solving by Substitution
(5, 3)
2x + y = 13
8x + 3y = 49
8x + 3( y )= 49
13 -2x
-2x
y = 13 – 2x
8x x = 49
2x + 39 = 49
y = 13 – 2( x ) 5
-39
2x = 10
y = 3
x = 5

10. The sum of two numbers is 82. One number is 12 more than the other
The sum of two numbers is 82. One number is 12 more than the other. What are the numbers?
Let x = the larger number and y the smaller.

11. The difference between two numbers is 9
The difference between two numbers is 9. Three times the larger number is six times the smaller. What are the numbers?

12. Homework tonight:
Page 365 (2-26) even