1.14: Past-paper question 2

4PM1/1R/June/2023 — Question 2 · 8 marks

One solution to the following simultaneous equations
y=px+96x2−xy=5\begin{aligned}y &= px + 9 \\ 6x^2 - xy &= 5\end{aligned}
is (−12,q)\displaystyle \left(-\frac{1}{2}, q\right), where p\displaystyle p is an integer and q\displaystyle q is a prime number.
(a) Find the value of p\displaystyle p and the value of q\displaystyle q
(4)
(b) Hence find the other solution to the equations.
(4)