Choose the correct answer from the given four options. If 2x+y&4x… - Vidyadip

MCQ

Choose the correct answer from the given four options. If $\begin{bmatrix}2\text{x}+\text{y}&4\text{x}\\5\text{x}-7&4\text{x}\end{bmatrix}=\begin{bmatrix}7&7\text{y}-13\\\text{y}&\text{x}+6\end{bmatrix},$ then the value of $x + y$ is :

A
$x = 3, y = 1$
✓
$x = 2, y = 3$
C
$x = 2, y = 4$
D
$x = 3, y = 3$

✓

Answer

Correct option: B.

$x = 2, y = 3$

We have, $\begin{bmatrix}2\text{x}+\text{y}&4\text{x}\\5\text{x}-7&4\text{x}\end{bmatrix}=\begin{bmatrix}7&7\text{y}-13\\\text{y}&\text{x}+6\end{bmatrix}$
$\Rightarrow 4x = x + 6$
$ \Rightarrow x = 2$
and $4x = 7y - 13$
$\Rightarrow 8 = 7y - 13$
$\Rightarrow y = 3$
$\therefore x + y = 2 + 3 = 5$

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