If \(\begin{bmatrix}x^2 - 4x&y\\2x - y&3\end{bmatrix} = \begin{bmatrix}-3&1\\5&3\end{bmatrix}\), then the value of \(x + y\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4
By equality of matrices, every pair of corresponding elements must be equal:
\(x^2 - 4x = -3\)
\(y = 1\)
\(2x - y = 5\)
The first equation gives
\(x^2 - 4x + 3 = 0\)
\((x - 1)(x - 3) = 0\)
\(x = 1 \text{ or } x = 3\)
With y = 1, the third equation gives
\(2x - 1 = 5\)
\(x = 3\)
So only x = 3 satisfies all the equations, and
\(x + y = 3 + 1 = 4\)
Why the other options are incorrect
Option (1) 2 — Incorrect. This takes x = 1, but then \(2x - y = 1\), not 5.
Option (2) 5 — Incorrect. With y = 1 this needs x = 4, but then \(x^2 - 4x = 0\), not \(-3\).
Option (3) 3 — Incorrect. With y = 1 this needs x = 2, but then \(x^2 - 4x = -4\), not \(-3\).