Question
Find $x$ and $y,$ if $\left(\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right)\left(\begin{array}{c}2 x \\ 1\end{array}\right)+2\left(\begin{array}{c}-4 \\ 5\end{array}\right)=4\left(\begin{array}{l}2 \\ y\end{array}\right)$
✓
Answer
$\begin{aligned} & \left(\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right)\binom{2 x}{1}+2\binom{-4}{5}=4\binom{2}{y} \end{aligned} $
$\begin{aligned} & \binom{6 x-2}{-2 x+4}+\binom{-8}{10}=\binom{8}{4 y} \end{aligned} $
$\begin{aligned} & \binom{6 x-10-8}{-2 x+14+10}=\binom{8}{4 y} \end{aligned} $
Now $6 x-10=8$
$\therefore 6 x=18$
$ \therefore x=\frac{18}{6}=3$
and
$-x+14=4 y$
$ -2 \times 3+14=4 y$
or
$4 y=14-6=8$
$ \therefore y=\frac{8}{4}=2$
$ \therefore x=3, y=2$
$\begin{aligned} & \binom{6 x-2}{-2 x+4}+\binom{-8}{10}=\binom{8}{4 y} \end{aligned} $
$\begin{aligned} & \binom{6 x-10-8}{-2 x+14+10}=\binom{8}{4 y} \end{aligned} $
Now $6 x-10=8$
$\therefore 6 x=18$
$ \therefore x=\frac{18}{6}=3$
and
$-x+14=4 y$
$ -2 \times 3+14=4 y$
or
$4 y=14-6=8$
$ \therefore y=\frac{8}{4}=2$
$ \therefore x=3, y=2$
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