JAMB 1997 · UME · Q23

Determine $x + y$ if $\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -1 \\ 8 \end{pmatrix}$ .

Worked solution (try it first)

Multiply out the left side to get two equations: $2x - 3y = -1$ and $-x + 4y = 8$ .
From the second, $x = 4y - 8$ .
Substitute into the first: $8y - 16 - 3y = -1$ , so $5y = 15$ and $y = 3$ .
Then $x = 12 - 8 = 4$ .
So $x + y = 7$ , option C.