2.3: Linear equations with 2\sqrt{2}

0606/21/O/N/19 — Question 4 · 5 marks

Do not use a calculator in this question.

Solve the following simultaneous equations, giving your answers for both xx and yy in the form a+b2a + b\sqrt{2}, where aa and bb are integers.
2x+y=52x + y = 53x2y=73x - \sqrt{2}\,y = 7
[5]