7.2: Solving Linear Systems by
Substitution
Integrated Math 2
Steps for Substitution
(1) Pick the easiest equation that has a 1x or 1y, solve
the equation for that variable
(2) Plug the expression on the right into the equation
that has not been used for the appropriate variable
- Make sure the same variable is in the equation
(3) Solve the equation for the first variable
(4) Plug the solution back into an equation to find the
other variable
- Any equation will work!!!
Solving for y first
x  y  4

4 x  y  1
x+y=4
-x
-x .
y = -x + 4
Plug the expression in and solve:
4x + y = 1
4x + 1(-x+4) = 1
4x + -x + 4 = 1
3x + 4 = 1
-4
-4
3x = -3
3
3
x = -1
Plug x back in to find y:
y = -x + 4
= -(-1) + 4
=5
So the final answer is (-1, 5)
(This is the exact point the lines would cross at
on a graph)
Example 2: Solve for x first
x  y  4

4 x  y  1
x+y=4
-y
-y
x = -y + 4
Plug in the expression and solve:
4x + y = 1
4(-y+4) + y = 1
-4y + 16 + y = 1
-3y + 16 = 1
-16 -16
-3y = -15
-3
-3
y=5
Plug y back in to find x:
x = -y + 4
= -(5) + 4
= -1
The answer is still (-1, 5)