Q16. - Algebra 2

Question

Solve each equation.

$\left[\begin{array}{ccc}2x& 3& 3z\end{array}\right]\mathbf{=}\left[\begin{array}{ccc}5& 3y& 9\end{array}\right]$

Step-by-Step Solution

Answer

The solution is $\left(\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{,}\mathbf{1}\mathbf{,}\mathbf{3}\right)$.

Step 1 – Description of step.

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

 $\begin{array}{c}2x=5\\ 3y=3\\ 3z=9\end{array}$

Step 2 – Description of step.

Divide each side of $2x=5$ by 2 to find the value of $x$.

 $\begin{array}{c}\frac{2x}{2}=\frac{5}{2}\\ x=2.5\end{array}$

Step 3 – Description of step.

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

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

Step 4 – Description of step.

Divide each side of $3z=9$ by 3 to find the value of $z$.

$\begin{array}{c}\frac{3z}{3}=\frac{9}{3}\\ z=3\end{array}$

Therefore, the solution is $\left(2.5,1,3\right)$.