
Example
Use elimination to find the solution of this system.
x  3y = 17 First equation
x + 8y = 52 Second equation
Solution
Add the two equations.

x  x 
 + 
3y 8y 
= = 
 
17 52 
0x 
+ 
5y 
= 

35 

Simplify. The xterms have been eliminated.
To solve for y, divide both sides by 5. To find the value of x, substitute 7 for y in either of
the original equations. Then solve for x.

5y
y 
= 35 = 7 
We will use the first equation.
Substitute 7 for y.
Multiply.
Add 21 to both sides.
The solution of the system is (4, 7).
To check the solution, substitute 4 for x and 7 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. 
x  3y
x  3(7)
x  21
x 
= 17 = 17
= 17
= 4 
In the two original equations in the previous
example, the coefficients of x were opposites.
Thus, when the equations were added, the
xterms were eliminated. 
1x  1x 
 + 
3y 8y 
= = 
 
17 52 


5y 
= 

35 

When the coefficients of neither variable are opposites, we choose a
variable. Then we multiply both sides of one (or both) equations by an
appropriate number (or numbers) to make the coefficients of that variable
opposites.Note:
The Multiplication Principle of Equality
enables us to multiply both sides of an
equation by the same nonzero number
without changing the solutions of the
equation.

