Q36. - Algebra 2

Question

What is the value of $\mathbf{y}$ if $\left[\begin{array}{c}3x\\ y+5\end{array}\right]\mathbf{=}\left[\begin{array}{c}9+y\\ x\end{array}\right]$?

 A. 2      B. 4      C. $\mathbf{-}\mathbf{3}$      D. $\mathbf{-}\mathbf{1}$

Step-by-Step Solution

Answer

The value of y is $\mathbf{-}\mathbf{3}$.

Step 1 – Description of step.

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

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

Step 2 – Description of step.

Substitute $y+5$ for x into $3x=9+y$ and simplify.

$\begin{array}{c}3\left(y+5\right)=9+y\\ 3y+15=9+y\\ 3y-y=9-15\\ 2y=-6\end{array}$

Step 3 – Description of step.

Divide each side of $2y=-6$ by 2 to find the value of $y$.

$\begin{array}{c}\frac{2y}{2}=\frac{-6}{2}\\ y=-3\end{array}$

Therefore, option C is the correct answer.