Question

Solve each equation.

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

Short answer

The solution is $\left(\mathbf{4}\mathbf{,}\mathbf{-}\mathbf{3}\right)$.

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.

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

– Description of step.

Multiply $x-3y=13$ by 2 and subtract $2x+y=5$ from the obtained equation.

$\begin{array}{c}2x-6y-\left(2x+y\right)=26-5\\ 2x-6y-2x-y=21\\ -7y=21\end{array}$

– Description of step.

Divide each side of $-7y=21$ by $-7$ to find the value of $y$.

$\begin{array}{c}\frac{-7y}{-7}=\frac{21}{-7}\\ y=-3\end{array}$

– Description of step.

Substitute $-3$for $y$into $x-3y=13$and simplify to find the value of $x$.

$\begin{array}{c}x-3\left(-3\right)=13\\ x+9=13\end{array}$

– Description of step.

Subtract 9 from both the sides of $x+9=13$and simplify.

$\begin{array}{c}x+9-9=13-9\\ x=4\end{array}$

Therefore, the solution is $\left(4,-3\right)$.