Question

Find the value of $x$ and $y$ if $\left[\begin{array}{cc}x+10& y^2+2y\\ 0& -4\end{array}\right]=\left[\begin{array}{cc}3x+4& 3\\ 0& y^2-5y\end{array}\right]$

Answer 1

$\begin{array}{c}\left(\begin{array}{cc}x+10& y^2+2y\\ 3& -4\end{array}\right)=\left(\begin{array}{cc}3x+4& 3\\ 0& y^2-5y\end{array}\right)\\ x+10=3x+4\\ 10-4=3x-x\\ 6=2x\\ x=3\\ y^2+2y=3\\ y^2+2y-3=0\\ y^2+3y-y-3=0\\ y\left(y-3\right)-1\left(y+3\right)=0\\ \left(y-1\right)\left(y+3\right)=0\\ y=1,-3\left(-3isnottaken\right)\end{array}$

The value of $x$ and $y$ is $(3,1)$

Hence, this is the answer.