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Q36.

Expert-verifiedFound in: Page 158

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 $\mathbf{-}\mathbf{3}$.

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

$\begin{array}{c}3x=9+y\\ y+5=x\end{array}$Substitute $y+5$ for *x* into $3x=9+y$ and simplify.

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

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.

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