Find y, if \(\begin{pmatrix}5 & -6 \\2 & -7\end{pmatrix}\begin{pmatrix}x \\ y \end{pmatrix} = \begin{pmatrix}7 \\-11\end{pmatrix}\)

Find y, if \(\begin{pmatrix}5 & -6 \\2 & -7\end{pmatrix}\begin{pmatrix}x \\ y \end{pmatrix} = \begin{pmatrix}7 \\-11\end{pmatrix}\)

JAMB 2014

Find y, if \(\begin{pmatrix}5 & -6 \\2 & -7\end{pmatrix}\begin{pmatrix}x \\ y \end{pmatrix} = \begin{pmatrix}7 \\-11\end{pmatrix}\)

A. 8
B. 5
C. 3
D. 2

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Correct Answer: Option C

Explanation

\(\begin{pmatrix}5 & -6 \\2 & -7\end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix}7 \\-11\end{pmatrix}\)

By matrices multiplication;

5x - 6y = 7 ........(1)
2x - 7y = -11 ......(2)
2 x (1): 10x - 12y = 14 .......(3)
5 x (2): 10x - 35y = -55 ......(4)

(3) - (4): 23y = 69

y = 69/23 = 3

There is an explanation video available below.

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