If $\left[\begin{array}{ccc}3 & 2 x+5 y & -2 \\ x+4 y & 7 & -5\end{array}\right]=\left[\begin{array}{rrr}3 & 10 & -2 \\ 2 & 7 & -5\end{array}\right]$. Then the values of x and y are:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) - $x=10, y=-2$
$\begin{bmatrix} 3 & 2x+5y & -2 \\ x+4y & 7 & -5 \end{bmatrix} = \begin{bmatrix} 3 & 10 & -2 \\ 2 & 7 & -5 \end{bmatrix}$
$2x + 5y = 10$
$x + 4y = 2$
$x = 2 - 4y$
$2(2 - 4y) + 5y = 10$
$4 - 8y + 5y = 10$
$4 - 3y = 10$
$-3y = 6 \Rightarrow y = -2$
$x = 2 - 4(-2) = 2 + 8 = 10$
The values are $x = 10,\; y = -2$.