A mixed xy term

7 written marks

Solve the system \(x+y=5\), \(x^2-xy+y^2=13\).

1. Use substitution to obtain a quadratic equation in \(x\).

   [3]

2. Find both ordered pairs \((x,y)\).

   [2]

3. Without using the coordinate values from part (b), show that \(xy=4\).

   [2]

Complete-answer checking, worked solutions and written marking guidance.