If \(\begin{bmatrix}x + 2y&3\\-1&2x - y\end{bmatrix} = \begin{bmatrix}8&3\\-1&1\end{bmatrix}\), then the value of \(x + y\) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5
Two matrices are equal when their corresponding elements are equal. Comparing the first-row, first-column and the second-row, second-column elements:
\(x + 2y = 8\)
\(2x - y = 1\)
From the second equation, \(y = 2x - 1\). Putting this in the first:
\(x + 4x - 2 = 8\)
\(5x = 10\)
\(x = 2\)
Then
\(y = 2(2) - 1 = 3\)
\(x + y = 2 + 3 = 5\)