1. Solving Systems of Equations by Substitution
Step 2
Step 3
Step 4
Step 5
Solve both equations for y (i.e., put in slope-intercept form).
Step 1
Set the two equations equal to each other (eliminate the y’s).
Solve for x.
Substitute the value of x into either of the original equations and solve for y.
Write the x and y values as an ordered pair(x, y), and check.

2. Example: 1
Solve the system by substitution.
y = x + 1
4x + y = 6
Solve both equations for y.
The first equation is solved for y.
Solve the second equation for y.
Step 1 y = x + 1
4x + y = 6
-4x x
y = -4x + 6
Step 2
x + 1 = -4x + 6
Set the 2 equations equal to each other (elimate the y’s).

3. Example: 1 continued
Solve the system by substitution.
y = x + 1
4x + y = 6
Step 3
x + 1 = -4x + 6
+4x x
5x + 1 = 6
5x = 5
x = 1
Solve for x.

4. Example: 1 Continued
Solve the system by substitution.
y = x + 1
4x + y = 6
Step 4
y = 1 + 1
y = 2
Substitute the value of x into either of the original equations and solve for y.
Step 5
(1, 2)
Write the x and y values as an ordered pair.

5.   Example: 1 Continued Solve the system by substitution. y = x + 1
4x + y = 6
Step 5 - continued
(1, 2)
Check the ordered pair.
Substitute (1, 2) into both equations in the system.
y = x + 1
2 2 
4x + y = 6
4(1)
6 6 

6. Example 2
Solve the system by substitution.
y = x + 3
y = 2x + 5
Step 1
y = x + 3
y = 2x + 5
Both equations are solved for y.
Step 2
x + 3 = 2x + 5
Set the 2 equations equal to each other (elimate the y’s).
-2x –2x
-x + 3 = 5
-x = 2
-x/-1 = 2/-1
x = -2
Step 3
x + 3 = 2x + 5
Solve for x.

7.   Example 2 Solve the system by substitution. y = x + 3 y = 2x + 5
Step 4
y =
y = 1
Substitute the value of x into either of the original equations and solve for y.
Step 5
(-2, 1)
Write the x and y values as an ordered pair and check.
y = x + 3
1 1 
y = 2x + 5
(-2) + 5
-4 + 5  1

8. Example 3
Solve the system by substitution.
y = 2x + 4
16x + 4y = 40
Step 1 y = 2x + 4
16x + 4y = 40
-16x x
4y = -16x + 40
y = -4x + 10

9. Example 3
Solve the system by substitution.
y = 2x + 4
16x + 4y = 40
Step 2
2x + 4 = -4x + 10
+4x x
6x + 4 = 10
6x = 6
6x/6 = 6/6
x = 1
Step 3
2x + 4 = -4x + 10

10.   Example 3 Solve the system by substitution. y = 2x + 4
16x + 4y = 40
Step 4
y = 2(1) + 4
y = 2 + 4
y = 6
Step 5
(1, 6)
y = 2x + 4
6 2(1) + 4
6 6 
16x + 4y = 40
16(1) + 4(6) 40 