# Exam-Style Question on Simultaneous Equations

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 321. This question is similar to one that appeared on a GCSE Higher paper in 2017. The use of a calculator is not allowed.

Two numbers are chosen so that the sum of their squares is 25.

If those numbers are represented by $$x$$ and $$y$$ they will also satisfy the equation:

$$y-3x=13$$

Use an algebraic method to find two possible values of $$x$$ and $$y$$ .

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If you need more practice try the self-checking interactive exercises called Simultaneous Equations level 7.

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