Question

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

Answer 1

$x\left[\begin{array}{c}2\\ 3\end{array}\right]+y\left[\begin{array}{c}-1\\ 1\end{array}\right]=\left[\begin{array}{c}10\\ 5\end{array}\right]$
$\Rightarrow \left[\begin{array}{c}2x\\ 3x\end{array}\right]+\left[\begin{array}{c}-y\\ y\end{array}\right]=\left[\begin{array}{c}10\\ 5\end{array}\right]$
$\Rightarrow \left[\begin{array}{c}2x-y\\ 3x+y\end{array}\right]=\left[\begin{array}{c}10\\ 5\end{array}\right]$
Comparing the corresponding elements of these two matrices,
we get $2x-y=10$ and $3x+y=5$
Solving these we get,
$x=3$ and $y=-4$