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Lesson 5 of 5

SHORTCUT

Two equations: elimination

Add or subtract the equations to make one letter disappear.

The question

Solve x + y = 10 and x − y = 4

The trick

Line the equations up and add or subtract them so that one letter cancels out completely.

Worked example

  1. 1Add the two equations: (x + y) + (x − y) = 10 + 4
  2. 2The y terms cancel: 2x = 14, so x = 7
  3. 3Substitute back into the first: 7 + y = 10, so y = 3

So: x = 7, y = 3

Remember it like this

Same signs subtract, opposite signs add. Look at the letter you want gone and decide from its two signs.

In the exam

If no coefficient matches, multiply one whole equation through first to make a pair match. Always substitute back into the *original* equation to find the second letter — substituting into your own working repeats any error you already made.

Why it works

Adding equals to equals keeps the statement true. Choosing to add when the coefficients are opposite makes one variable vanish, leaving a simple one-variable equation.

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Try it yourself

0/3 correct
  • 1

    x + y = 12 and x − y = 2. What is x?

  • 2

    x + y = 12 and x − y = 2. What is y?

  • 3

    2x + y = 13 and x − y = 2. What is x?