Question

Solve for x and y if $(\begin{array}{c}2x+y\\ x-3y\end{array})=(\begin{array}{c}5\\ 13\end{array})$

Answer 1

$\left[\begin{array}{c}2x+y\\ x-3y\end{array}\right]=\left[\begin{array}{c}5\\ 13\end{array}\right]$

Comparing both sides, we get

$\Rightarrow 2x+y=5\to \left(1\right)$

$\Rightarrow x-3y=13\to \left(2\right)$

Multiplying second equation by $2$ $\&$ subtracting from $\left(1\right),$ we get

$2x+y=5\underset{–}{x-3y=13---}4y=-8$

$\Rightarrow y=-2$

Put $y=-2$ in equation $\left(1\right),$ we get

$\Rightarrow 2x-2=5$

$\Rightarrow 2x=7$

$\Rightarrow x=\frac{7}{2}$

Hence, the answer is $x=\frac{7}{2},y=-2.$