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Q36.

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Found in: Page 158

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# 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. localid="1648213664321" $\mathbf{-}\mathbf{1}$

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

See the step by step solution

## 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.