Systems of equations, step by step

Two equations, two letters, and one pair of numbers that satisfies both.

The question

6x + 12y = 182x − 12y = 22

6x + 12y = 18 2x − 12y = 22

6x + 12y = 18

2x − 12y = 22

6x + 12y = 18

2x − 12y = 22

6x + 12y = 18

2x − 12y = 22

8x = 40

x=5

y=−1

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: 12y in the first and −12y 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 8x = 40.
One letter left. 40 ÷ 8 = 5, so x = 5.
Now put x back into either equation to get y — this is the half that gets forgotten. It gives y = −1, so the solution is (5, −1).

How it works.

01
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.
02
Look at the y terms: 12y in the first and −12y in the second. They are opposites, so adding the two equations makes them cancel.
03
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 8x = 40.
04
One letter left. 40 ÷ 8 = 5, so x = 5.
05
Now put x back into either equation to get y — this is the half that gets forgotten. It gives y = −1, so the solution is (5, −1).