1. 9.7 Solving Systems of Equations Algebraically

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. 3 things can happen
1.) One solution 2.) many solutions (if variables cancel out leaving you with a true equation) 3.) no solution (if variables cancel out leaving you with a false equation)

4. 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

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

6. Solve by Substitution
Infinitely Many Solutions

7. If one equation is not solved for a variable….
Then you can solve for either x or y and then substitute

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. Solve by Substitution

13. Homework
Page 428 (8-21) all