Target Mathematics

1.13: Simultaneous equations

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)\left(-\frac{1}{2}, q\right), where pp is an integer and qq is a prime number.
(a) Find the value of pp and the value of qq
(4)
(b) Hence find the other solution to the equations.
(4)