Elimination adds or subtracts two equations so that one letter disappears. These free printable worksheets give pairs where that works cleanly, with whole-number answers for both letters.
If one equation has +9y and the other has −9y, adding them leaves an equation in x alone. That is the whole idea, and the skill is spotting which operation makes the cancellation happen — add when the signs differ, subtract when they match. Getting that backwards doubles the term instead of removing it, which is visible immediately.
Why this sheet works
The half that gets forgotten is the second letter. Finding x = 3 is not the answer; putting 3 back into either original equation and finding y is. A solution to a pair of equations is a pair of numbers, and an answer with one number in it is half done however correct that number is.
How this one works
One question from this sheet, worked through a step at a time.
−8x + 10y = −20 10x − 10y = 30
−8x + 10y = −20
10x − 10y = 30
−8x + 10y = −20
10x − 10y = 30
−8x + 10y = −20
10x − 10y = 30
2x = 10
2x = 10
x=5
x=5
y=2
Two equations, two letters. Neither one can be solved on its own — so the first move, whichever method you use, is to get down to ONE equation with ONE letter in it.
Look at the y terms: 10y in the first and −10y in the second. They are opposites, so adding the two equations makes them cancel.
Adding is allowed because both sides of each equation are equal — adding left to left and right to right keeps the balance, the same as adding a number to both sides. That gives 2x = 10.
One letter left. 10 ÷ 2 = 5, so x = 5.
Now put x back into either equation to get y — this is the half that gets forgotten. It gives y = 2, so the solution is (5, 2).
