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Simultaneous equations practice questions

Solve simultaneous equations by elimination: line the equations up, add or subtract to cancel one unknown, solve for the other, then substitute back. For x plus y equals 11 and x minus y equals 3, adding gives 2x equals 14, so x is 7 and y is 4.

Simultaneous equations are two equations solved together to find two unknowns. The elimination method is the most reliable under exam conditions, because it needs no rearranging.

Year 9GCSE FoundationGCSE Higher

The method, step by step

  1. Line the equations up. Write them one above the other with matching terms in columns.
  2. Look for a cancelling pair. If one unknown has equal and opposite coefficients, adding removes it.
  3. Multiply if needed. Scale one equation so a pair matches.
  4. Add or subtract. This leaves a single equation with one unknown.
  5. Substitute back. Put your answer into the simpler original equation to find the other unknown.

Worked example

Solve x + y = 11 and x − y = 3
The y terms are +y and −y, so adding the equations eliminates y.
Adding gives 2x = 14, so x = 7.
Substitute into x + y = 11: 7 + y = 11, so y = 4.
x = 7 and y = 4

Common mistakes

Subtracting when adding was needed. Check the signs of the matching pair before deciding.

Finding one unknown and stopping. Both are needed for full marks.

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