Question

If \[\begin{bmatrix}2x + y & 4x \\ 5x - 7 & 4x\end{bmatrix} = \begin{bmatrix}7 & 7y - 13 \\ y & x + 6\end{bmatrix}\] 

Options

• x = 3 , y =-1

• x = 2 , y= 3

• x= 2 , y= 4

• x = 3, y= 3

Answer 1

\[\begin{bmatrix}2x + y & 4x \\ 5x - 7 & 4x\end{bmatrix} = \begin{bmatrix}7 & 7y - 13 \\ y & x + 6\end{bmatrix}\]

Corresponding elements of equal matrices are equal . 

\[ \therefore 4x = \text{x + 6 and 2x + y} = 7\]

\[ \Rightarrow 3x = \text{6 and 2x + y} = 7\]

\[ \Rightarrow x = \text{2 and 2x + y }= 7\]

\[ \Rightarrow x = \text{2 and 2 ×2  + y }= 7\]

\[ \Rightarrow x = \text{2 and y } =7 - 4\]

\[ \Rightarrow x = \text{2 and y} = 3\]

Therefore, x = 2, y = 3.

Hence, the correct option is (b).