Solving Linear Systems of Equations by Substitution
Example
Use substitution to find the solution of this system.
3x + 4y
x  6y 
= 17 = 8 
First equation
Second equation 
Solution
Step 1 Solve one equation for one of the variables in terms of the
other variable.
Either equation may be solved for either variable.
For instance, letâ€™s solve the second equation for x.
Add 6y to both sides. 
x  6y
x 
= 8
= 6y  8 
Step 2 Substitute the expression found in Step 1 into
the other equation. Then, solve for the variable.
Substitute 6y  8 for x in the first equation.
Remove parentheses.
Combine like terms.
Subtract 24 from both sides.
Divide both sides by 14.
Now we know
.
Next, we will find x. 
3x + 4y
3(6y  8) + 4y
18y + 24 + 4y
14y + 24
14y
y 
= 17 = 17
= 17
= 17
= 7

Step 3 Substitute the value obtained in Step 2 into one of the equations
containing both variables. Then, solve for the remaining
variable.
We will use the equation from Step 1.

x 
= 6y  8 
Substitute
for y.

x


Simplify.
The solution of the system is

x 
= 5 
Step 4 To check the solution, substitute it into each original equation.
Then simplify.
Substitute 5 for x and
for y into each original equation.
Then simplify.
In each case, the result will be a true statement.
The details of the check are left to you.
Note:
If we graphed the system, the lines would
intersect at the point
