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

Question

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:

x = 3, y = 1
x = 2, y = 3
x = 2, y = 4
x = 3, y = 3

✓

Answer

x = 2, y = 3

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

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