Find y, if (5−62−7)(52)=(7−11)

Find y, if $\left(\begin{array}{cc}5& -6\\ 2& -7\end{array}\right)\left(\begin{array}{c}5\\ 2\end{array}\right)=\left(\begin{array}{c}7\\ -11\end{array}\right)$

Answer Details

$\left(\begin{array}{cc}5& -6\\ 2& -7\end{array}\right)\left(\begin{array}{c}5\\ 2\end{array}\right)=\left(\begin{array}{c}7\\ -11\end{array}\right)$
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