If \(\begin{bmatrix}2&1\\3&2\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}5\\8\end{bmatrix}\), then the values of x and y are
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(x = 2,\ y = 1\)
Multiplying row by column on the left side:
\( \displaystyle \begin{bmatrix}2x + y\\3x + 2y\end{bmatrix} = \begin{bmatrix}5\\8\end{bmatrix} \)
By equality of matrices:
\(2x + y = 5\)
\(3x + 2y = 8\)
Multiplying the first equation by 2 and subtracting the second:
\(4x - 3x = 10 - 8\)
\(x = 2\)
Then
\(y = 5 - 2x = 1\)
Why the other options are incorrect
Option (2) \(x = 1,\ y = 3\) — Incorrect. It satisfies \(2x + y = 5\), but \(3x + 2y = 9\), not 8.
Option (3) \(x = 3,\ y = -1\) — Incorrect. It satisfies \(2x + y = 5\), but \(3x + 2y = 7\), not 8.
Option (4) \(x = 1,\ y = 2\) — Incorrect. This gives \(2x + y = 4\), not 5; the values of x and y have been interchanged.