JAMB 2014 · UTME · Q22

Find $y$ if $\begin{pmatrix} 5 & -6 \\ 2 & -7 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 7 \\ -11 \end{pmatrix}$ .

Worked solution (try it first)

Multiply out the left side to get two equations: $5x - 6y = 7$ and $2x - 7y = -11$ .
Make the $x$ terms match: multiply the first by 2 and the second by 5, giving $10x - 12y = 14$ and $10x - 35y = -55$ .
Subtract the second from the first: $23y = 69$ , so $y = 3$ , option D.