Question

Solve for x and y if $\left(\begin{array}{c}{y}^2\\ x^2\end{array}\right)+2\left(\begin{array}{c}3y\\ 2x\end{array}\right)=3\left(\begin{array}{c}-3\\ 7\end{array}\right)$

Answer 1

$\left(\begin{array}{c}{y}^2\\ x^2\end{array}\right)+2\left(\begin{array}{c}3y\\ 2x\end{array}\right)=3\left(\begin{array}{c}-3\\ 7\end{array}\right)$

$\left(\begin{array}{c}{y}^2\\ x^2\end{array}\right)+\left(\begin{array}{c}6y\\ 4x\end{array}\right)=\left(\begin{array}{c}-9\\ 21\end{array}\right)$

$\left(\begin{array}{c}{y}^2+6y\\ x^2+4x\end{array}\right)=\left(\begin{array}{c}-9\\ 21\end{array}\right)$

Equating corresponding elements of equal matrices, we get
$x^2+4x=21$
$\Rightarrow x^2+4x-21=0$
$\Rightarrow x^2+7x-3x-21=0$
$\Rightarrow x(x+7)-3(x+7)=0$
$\Rightarrow (x+7)(x-3)=0$
$\Rightarrow x=-7,3$
$y^2+6y=-9$
$y^2+6y+9=0$
$(y+3{)}^2=0$
$y+3=0$
$y=-3$