Find the values of $x$ and $y$ from the following equation: $2 \begin{bmatrix} x & 5 \\ 7 & y-3 \end{bmatrix} + \begin{bmatrix} 3 & -4 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 7 & 6 \\ 15 & 14 \end{bmatrix}$

$x = 2, \quad y = 9$

The correct answer is Option (3) → $x = 2, \quad y = 9$ ##

We have

$2 \begin{bmatrix} x & 5 \\ 7 & y-3 \end{bmatrix} + \begin{bmatrix} 3 & -4 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 7 & 6 \\ 15 & 14 \end{bmatrix} \Rightarrow \begin{bmatrix} 2x & 10 \\ 14 & 2y-6 \end{bmatrix} + \begin{bmatrix} 3 & -4 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 7 & 6 \\ 15 & 14 \end{bmatrix}$

or $\quad \begin{bmatrix} 2x + 3 & 10 - 4 \\ 14 + 1 & 2y - 6 + 2 \end{bmatrix} = \begin{bmatrix} 7 & 6 \\ 15 & 14 \end{bmatrix} \Rightarrow \begin{bmatrix} 2x + 3 & 6 \\ 15 & 2y - 4 \end{bmatrix} = \begin{bmatrix} 7 & 6 \\ 15 & 14 \end{bmatrix}$

or $\quad 2x + 3 = 7 \quad \quad \text{and} \quad \quad 2y - 4 = 14$

or $\quad 2x = 7 - 3 \quad \quad \text{and} \quad \quad 2y = 18$

or $\quad x = \frac{4}{2} \quad \quad \quad \text{and} \quad \quad y = \frac{18}{2}$

i.e. $\quad x = 2 \quad \quad \quad \text{and} \quad \quad y = 9.$