Question

Solve each equation.

$\left[\begin{array}{cc}9& 13\end{array}\right]\mathbf{=}\left[\begin{array}{cc}x+2y& 4x+1\end{array}\right]$

Short answer

The solution is $\left(\mathbf{3}\mathbf{,}\mathbf{3}\right)$.

Step-by-step solution

– Description of step.

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

$\begin{array}{c}x+2y=9\\ 4x+1=13\end{array}$

– Description of step.

Subtract 1 from both the sides of $4x+1=13$ and simplify.

$\begin{array}{c}4x+1-1=13-1\\ 4x=12\end{array}$

– Description of step.

Divide each side of $4x=12$by 4 to find the value of x.

$\begin{array}{c}\frac{4x}{4}=\frac{12}{4}\\ x=3\end{array}$

– Description of step.

Substitute 3 for x into $x+2y=9$ and simplify.

$\begin{array}{c}3+2y=9\\ 2y=9-3\\ 2y=6\end{array}$

– Description of step.

Divide each side of $2y=6$by 2 and simplify to find the value of $y$.

$\begin{array}{c}\frac{2y}{2}=\frac{6}{2}\\ y=3\end{array}$

Therefore, the solution is $\left(3,3\right)$.