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
$\left(\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right)\left(\begin{array}{c}2 x \\ 1\end{array}\right)+2\left(\begin{array}{c}-4 \\ 5\end{array}\right)=4\left(\begin{array}{l}2 \\ y\end{array}\right)$
$\left(\begin{array}{c}6 x-2 \\ -2 x+4\end{array}\right)+\left(\begin{array}{c}-8 \\ 10\end{array}\right)=\left(\begin{array}{c}8 \\ 4 y\end{array}\right)$
$\left(\begin{array}{c}6 x-10-8 \\ -2 x+14+10\end{array}\right)=\left(\begin{array}{c}8 \\ 4 y\end{array}\right)$
$\text { Now } 6 x-10=8$
$\therefore 6 x=18$
$\therefore x=\frac{18}{6}=3$
and
$-x + 14 = 4y$
$-2 x^3 + 14 = 4y$
or
$4y = 14 - 6 = 8$
$\therefore y=\frac{8}{4}=2$
$\therefore x=3, y=2$
$\left(\begin{array}{c}6 x-2 \\ -2 x+4\end{array}\right)+\left(\begin{array}{c}-8 \\ 10\end{array}\right)=\left(\begin{array}{c}8 \\ 4 y\end{array}\right)$
$\left(\begin{array}{c}6 x-10-8 \\ -2 x+14+10\end{array}\right)=\left(\begin{array}{c}8 \\ 4 y\end{array}\right)$
$\text { Now } 6 x-10=8$
$\therefore 6 x=18$
$\therefore x=\frac{18}{6}=3$
and
$-x + 14 = 4y$
$-2 x^3 + 14 = 4y$
or
$4y = 14 - 6 = 8$
$\therefore y=\frac{8}{4}=2$
$\therefore x=3, y=2$
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