Q17. - Algebra 2

Question

Solve each equation.

$\left[\begin{array}{cc}4x& 3y\end{array}\right]\mathbf{=}\left[\begin{array}{cc}12& -1\end{array}\right]$

Step-by-Step Solution

Answer

The solution is $\left(\mathbf{3}\mathbf{,}\mathbf{-}\frac{1}{3}\right)$.

Step 1 – Description of step.

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

$\begin{array}{c}4x=12\\ 3y=-1\end{array}$

Step 2 – Description of step.

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

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

Step 3 – Description of step.

Divide each side of $3y=-1$ by 3 to find the value of y.

$\begin{array}{c}\frac{3y}{3}=\frac{-1}{3}\\ y=\frac{-1}{3}\end{array}$

Therefore, the solution is $\left(3,-\frac{1}{3}\right)$.