Problem

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

A rectangular sports pitch has length $x$ metres and width $y$ metres, where $x>y$.

Given that the perimeter of the pitch is $350$ m,

(a) write down an equation linking $x$ and $y$.

Given also that the area of the pitch is $7350$ m$^2$,

(b) write down a second equation linking $x$ and $y$.

(c) hence find the value of $x$ and the value of $y$.