Basic Geometry

The diagram shows two congruent triangles \(PQR\) and \(XYR\). Triangle \(XYR\) is an isosceles triangle such that \(XR = YR\).

1. Write down two simultaneous equations, in the form \(ax + by = k\), where \(a\), \(b\) and \(k\) are constants, to represent this information.

   [2]

2. Solve the simultaneous equations to find the length of \(PQ\).

   [3]