NECO 2023 · Paper 1 · Q13

Matrices & linear transformations

If $\begin{pmatrix} 3 & -1 \\ 1 & 1 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 13 \\ 7 \end{pmatrix}$ , find the value of $y$ .

Worked solution (try it first)

Each row times the column gives one equation: $3x - y = 13$ and $x + y = 7$ .
Add the two equations to remove $y$ : $4x = 20$ , so $x = 5$ .
Then $y = 7 - 5 = 2$ , option B.

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