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 the value of $x$ and $y$.

Answer 1

Given,

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

From this matrix equation we get,

$2x-y=10$.....(1) and $3x+y=5$.....(2).

Now adding (1) and (2) we get,

$5x=15$

or, $x=3$.

Now putting this in (1) we get, $y=-4$.