1. 7.2 Solving Systems of Equations by Substitution
What you’ll learn:
1. To solve systems of equations using substitution.

2. To solve a system by substitution:
Solve one equation for one of the variables (x or y.)
Plug into the other equation what that variable is equal to.
Solve that equation.
If you found y, plug y into the other equation to find x and vice-versa. (Remember that the solution should be an ordered pair, so you have to find x and y.
If your variable cancels and a false statement remains, there is no solution. If your variable cancels and a true statement remains, the solution is “infinitely many.”

3. Example: 4x+y=12 -2x-3y=14 y=-4x+12 -2x-3(-4x+12)=14 x=4y
y=-8 solution: (5,-8)
Check: 4(5)+(-8)=12
-2(5)-3(-8)=14
Example:
x=4y
4x-y=75
4(4y)-y=75
16y-y=75
15y=75
y=5
x=4(5)
x=20
Solution: (20,5)
Check: 20=4(5)
4(20)-5=75

4. More Examples c-4d=1 2c-8d=2 Solve 1st equ. for c c=4d+1 2x+2y=8
Plug into 2nd equ
2(4d+1)-8d=2
8d+2-8d=2
2=2
Infinitely many
More Examples
2x+2y=8
x+y=-2
Solve 2nd equ. for y
y=-x-2
Plug into 1st equ. in place of y
2x+2(-x-2)=8
2x-2x-4=8
-4=8
No solution

5. Word Problems
Write a system and solve: Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $ How many adults tickets and student tickets were purchased? x=adults tickets, y=student tickets x+y=8 7.25x+5.50y=52.75 y=-x x+5.50(-x+8)= x-5.50x+44= x=8.75 x=5, y=3

6. Homework p even