Question
Find $x$ and $y$ if $[3 \ x \ 8]\left[\begin{array}{ll}1 & 4 \\ 3 & 7\end{array}\right]-3\left[\begin{array}{ll}2 & -7\end{array}\right]=5\left[\begin{array}{ll}3 & 2 y\end{array}\right]$
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Answer
$[3 \ x, 8]\left[\begin{array}{ll}1 & 4 \\ 3 & 7\end{array}\right]-3\left[\begin{array}{ll}2 & -7\end{array}\right]=5\left[\begin{array}{ll}3 & 2 y\end{array}\right]$
$ {[3 x+24,12 x+56]-[6,-21]=\left[15 10 y\right]}$
$ {[3 x+24-6,12 x+56+21]=\left[15 10 y\right]}$
$ {[3 x+1812 x+77]=\left[15 10 y\right]}$
Comaring the corresspoing elements we get
$3 x+18=15$
$ =3 x=-3$
$ =x=-1$
$ 12 x+77=10 y$
$ =10 y=-12+77=65$
$ =y=6.5$
$ {[3 x+24,12 x+56]-[6,-21]=\left[15 10 y\right]}$
$ {[3 x+24-6,12 x+56+21]=\left[15 10 y\right]}$
$ {[3 x+1812 x+77]=\left[15 10 y\right]}$
Comaring the corresspoing elements we get
$3 x+18=15$
$ =3 x=-3$
$ =x=-1$
$ 12 x+77=10 y$
$ =10 y=-12+77=65$
$ =y=6.5$
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