find values of x and y.


If $x\left[\begin{array}{l}2 \\ 3\end{array}\right]+y\left[\begin{array}{c}-1 \\ 1\end{array}\right]=\left[\begin{array}{c}10 \\ 5\end{array}\right]$, find values of $x$ and $y$.


$x\left[\begin{array}{l}2 \\ 3\end{array}\right]+y\left[\begin{array}{c}-1 \\ 1\end{array}\right]=\left[\begin{array}{l}10 \\ 5\end{array}\right]$

$\Rightarrow\left[\begin{array}{l}2 x \\ 3 x\end{array}\right]+\left[\begin{array}{c}-y \\ y\end{array}\right]=\left[\begin{array}{l}10 \\ 5\end{array}\right]$

$\Rightarrow\left[\begin{array}{l}2 x-y \\ 3 x+y\end{array}\right]=\left[\begin{array}{l}10 \\ 5\end{array}\right]$

Comparing the corresponding elements of these two matrices, we get:

2x − y = 10 and 3x + y = 5

Adding these two equations, we have:


5x = 15

$\Rightarrow x=3$

Now, $3 x+y=5$

$\Rightarrow y=5-3 x$

$\Rightarrow y=5-9=-4$


$\therefore x=3$ and $y=-4$

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