Q22. - Algebra 2

Question

Solve each equation.

$\left[\begin{array}{c}2x\\ 2x+3y\end{array}\right]\mathbf{=}\left[\begin{array}{c}y\\ 12\end{array}\right]$

Step-by-Step Solution

Answer

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

Step 1 – Description of step.

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

$\begin{array}{c}2x=y\\ 2x+3y=12\end{array}$

Step 2 – Description of step.

Substitute $2x$ for $y$ into $2x+3y=12$ and simplify.

$\begin{array}{c}2x+3\left(2x\right)=12\\ 2x+6x=12\\ 8x=12\end{array}$

Step 3 – Description of step.

Divide each side of $8x=12$ by 8 to find the value of $x$.

$\begin{array}{c}\frac{8x}{8}=\frac{12}{8}\\ x=\frac{3}{2}\end{array}$

Step 4 – Description of step.

Substitute $\frac{3}{2}$ for $x$ into $2x=y$ and simplify to find the value of $y$.

$\begin{array}{c}2\left(\frac{3}{2}\right)=y\\ 3=y\end{array}$

Therefore, the solution is $\left(\frac{3}{2},3\right)$.