M1 2017 1 Edexcel

1

If the particle is in equilibrium, the forces add to 0, so:

\begin{pmatrix}15 \\ 1\end{pmatrix} + \begin{pmatrix}5q \\ -p\end{pmatrix} + \begin{pmatrix}-3p \\ -q\end{pmatrix} = \begin{pmatrix}0 \\ 0\end{pmatrix}

So 3p - 5q = 15 and p + q = 1. So q = 1 -p, giving 3p - 5(1 - p) = 15, so 8p - 5 = 15, so p = \dfrac 5 2 and q = -\dfrac 3 2.