Elimination Method (Level 2)           page 3 of 5

Example 1

Solve the system.   2x - 5y = 6   and  3x + y = 26

Step 1: Use multiplication to create terms that are opposites. 
We can create opposites by multiplying the entire 2nd equation by 5.  This will give us a 5y and a -5y that will cancel.

Step 2: Add the equations vertically.
Now that we've created terms that are opposites, one of the variables will cancel out when we add the equations.

Step 3: Solve for the first variable.​
The y terms canceled, so we can solve the equation that's left.

Step 4: Solve for the second variable.
Go back to one of the original equations (you can choose either one) and plug in 8 for x.

Step 5: Write answer as ordered pair.
Make sure to put the variables in alphabetical order when you write the ordered pair.

Step 6: Check your answer.
Use the original equation that you didn't use earlier. If you use the same equation twice, it will not find a mistake.

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