Question

Solve each equation.

$\left[\begin{array}{cc}{\mathbf{x}}^2\mathbf{+}\mathbf{1}& 5-y\\ x+y& y-4\end{array}\right]\mathbf{=}\left[\begin{array}{cc}5& x\\ 5& 3\end{array}\right]$

Short answer

The solution is $\left(-2,7\right)$.

Step-by-step solution

– Description of step.

As the matrices are equal, the corresponding elements are equal. Write the four linear equations to show this equality.

$\begin{array}{c}{x}^2+1=5\\ 5-y=x\\ x+y=5\\ y-4=3\end{array}$

– Description of step.

Add 4 on both the sides of $y-4=3$ and simplify.

$\begin{array}{c}y-4+4=3+4\\ y=7\end{array}$

– Description of step.

Substitute $7$ for $y$ into $5-y=x$and simplify.

$\begin{array}{c}5-7=x\\ -2=x\end{array}$

Therefore, the solution is $\left(-2,7\right)$.