1. Solving Systems Using Substitution

2. Substitution Sometimes you don’t have a graphing calculator to use.
Substitution allows you to solve a one-variable equation.
One of the equations should be in either y = or x = form.
Replace that variable in the other equation with the stuff on the right side.

3. Example 1 Solve y = 2x and 7x – y = 15
Replace the y in the second equation with what y is equal to in the first equation
7x – (2x) = 15
Simplify: 5x = 15
Solve: x = 3
Now, replace x in either equation with 3 to find y y = 2(3)
y = 6 so the solution is (3, 6)
Check in the second equation 7(3) – (6) = 15
21 – 6 = 15 is true so the solution is (3, 6)

4. Example 2 Solve: y = x + 5 and 4x + y = 20
Replace the y in the second equation with “x + 5”
4x + (x + 5) = 20
Simplify: 5x + 5 = 20
Solve: 5x = x = 3
Replace the x in the first equation with 3
y = 3 + 5
y = 8
(3, 8)
Check your results.

5. Example 3 Solve: x = -2y – 1 and 4x – 4y = 20
Replace the x in the second equation with “-2y – 1”
4(-2y – 1) – 4y = 20 Distribute
-8y – 4 – 4y = 20 Simplify
-12y – 4 = 20 Solve
-12y = y = -2
Replace the y in the first equation with 2
x = -2(-2) - 1
x = 3
(3, -2)
Check your work.

6. Example 4 Solve: y = 2x + 3 and x – 2y = 3
Replace y with 2x + 3 in the second equation.
x – 2(2x + 3) = 3
Distribute the –2 x – 4x – 6 = 3
Simplify x – 6 = 3
Solve x = x = -3
Replace x with –3 in the first equation
y = 2(-3) y = -3
So, the solution is (-3, -3) (Check it in the 2nd equation too.)

7. Try these… x + y = 38 x = 2y – 25 y = x + 2.8 y + 4.6 = 2x y = x + 4
(17, 21)
(7.4, 10.2)
(1, 5)
(20, 70)