Q6. - Algebra 2

Question

Solve each equation.

$\left[\begin{array}{c}\mathbf{x}\mathbf{+}\mathbf{4}\\ \mathbf{2}\mathit{y}\end{array}\right]\mathbf{=}\left[\begin{array}{c}\mathbf{9}\\ \mathbf{12}\end{array}\right]$

Step-by-Step Solution

Answer

The solution is $\left(\mathbf{5}\mathbf{,}\mathbf{6}\right)$.

Step 1 – Description of step.

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

 $\begin{array}{c}x+4=9\\ 2y=12\end{array}$

Step 2 – Description of step.

Divide each side of $2y=12$ by 2 to find the value of $y$.

 $\begin{array}{c}\frac{2y}{2}=\frac{12}{2}\\ y=6\end{array}$

Step 3 – Description of step.

Subtract 4 from both the sides of $x+4=9$ and simplify to find the value of x.

$\begin{array}{c}x+4-4=9-4\\ x=5\end{array}$

Therefore, the solution is $\left(5,6\right)$.