if

Question:

If $2\left[\begin{array}{ll}3 & 4 \\ 5 & x\end{array}\right]+\left[\begin{array}{ll}1 & y \\ 0 & 1\end{array}\right]=\left[\begin{array}{rr}7 & 0 \\ 10 & 5\end{array}\right]$, find $x$ and $y$

Solution:

Given : $2\left[\begin{array}{ll}3 & 4 \\ 5 & x\end{array}\right]+\left[\begin{array}{cc}1 & y \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right]$

$\Rightarrow\left[\begin{array}{cc}6 & 8 \\ 10 & 2 x\end{array}\right]+\left[\begin{array}{ll}1 & y \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right]$

$\Rightarrow\left[\begin{array}{cc}6+1 & 8+y \\ 10+0 & 2 x+1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right]$

$\Rightarrow\left[\begin{array}{cc}7 & 8+y \\ 10 & 2 x+1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right]$

$\therefore 8+y=0$

$\Rightarrow y=-8$

Also,

$2 x+1=5$

$\Rightarrow 2 x=4$

$\Rightarrow x=\frac{4}{2}=2$

$\therefore x=2$ and $y=-8$

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