1. Solving Systems Using Substitution
Chapter 7 Section 2
Solving Systems Using Substitution

2. Substitution allows you to create a one variable equation
Steps
Pick one equation and substitute its x or y
value into the other equation
Solve for the variable that is left
Substitute the solution into the equation that
you did not change and solve for the
remaining variable
Check to see if solution satisfies both
equations

3. 1 Examples Step 1 Step 2 Step 3 y = x + 6.1 Step 4 y = -2x – 1.4
x = -2x – 1.4
+2x x
3x = -1.4
– –6.1
3x = -7.5
x =
y = -2(-2.5) – 1.4
y = 5 – 1.4
y = 3.6
y = x y = -2x – 1.4
3.6= =-2(-2.5) – 1.4
3.6 = = 5 – 1.4
3.6 = 3.6
The solution is (-2.5, 3.6)

4. 2 1 car 3 vans 4 drivers and 22 students going on field trip –
vans seat 6 - cars seat 4. How many cars and
vans are needed for the trip?
6v + 4c = 22
6(-c + 4) + 4c = 22
-6c c = 22
-2c + 24 = 22
– 24 – 24
-2c = -2
c = 1
v = # of vans
c = # of cars
v + c = 4
6v + 4c = 22
Solve by substitution
6v + 4(1) = 22
6v + 4 = 22
– 4 – 4
6v = 18
v = 3
v + c = 4
– c – c
v = -c + 4
1 car
3 vans 4

5. 3 No solution x + y = 6 5x + 5y = 10 5x + 5y = 10 5(-y + 6) + 5y = 10
30 = 10
Solve for x
x + y = 6
– y – y
x = -y + 6
No solution

6. infinite # of solutions
To determine how many solutions a system has, refer to this chart of results
2 = 2
infinite # of solutions
10 ≠ 1
no solutions
x = 4
one solution 6

7. Questions?
Ask now!

8. Assignments
Class work
Page #1 – 4, 5 – 21 odd,
Page #25 – 31 odd,
Homework
Finish Class Work; Page 386 #46 – 48