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Simultaneous equations Cambridge IGCSE Mathematics revision

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In plain words

One equation with two unknowns has endless answers. Two equations pin it down to one pair of values that works in both. The idea is always the same: get rid of one letter so you're left with an equation you can solve.

Three things to know

  1. Elimination: make the number of x's (or y's) the same in both equations, then add or subtract the equations to remove that letter.
  2. Substitution: rearrange one equation to make a letter the subject, and put that into the other.
  3. Once you have one value, put it back in to find the other, and check in both equations.

Worked example

Solve 2x + y = 11 and x − y = 1.

  1. Add the two equations: the y's cancel, leaving 3x = 12.
  2. x = 4.
  3. Put x = 4 into x − y = 1: 4 − y = 1, so y = 3.

Tips and tricks

  • Same Signs Subtract. If the matching terms have different signs, add.
  • Give both values. An answer with only x gets only some of the marks.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Simultaneous equations: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. Solve x + y = 7 and x − y = 1. What is x?
    • 3
    • 4 (the answer)
    • 6
    • 8

    Adding gives 2x = 8.

  2. If 2x + y = 9 and y = 3, what is x?
    • 2
    • 3 (the answer)
    • 6
    • 12

    2x = 6.

  3. If y = 2x and x + y = 12, what is x?
    • 3
    • 4 (the answer)
    • 6
    • 8

    x + 2x = 12.

  4. Solve 3x + y = 10 and x + y = 4. What is x?
    • 2
    • 3 (the answer)
    • 6
    • 7

    Subtracting gives 2x = 6.

  5. How many solutions do two straight lines that cross have?
    • none
    • one (the answer)
    • two
    • infinitely many

    The solution is the point where they meet.

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