The values of x and y in \(\begin{bmatrix}2x+y\\ x+2y\end{bmatrix}=\begin{bmatrix}4\\ 5\end{bmatrix}\) are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1, 2
By equality of matrices, the corresponding entries are equal:
\(2x+y = 4\) … (1)
\(x+2y = 5\) … (2)
2 × (2) − (1):
\((2x+4y)-(2x+y) = 10-4\)
\(3y = 6,\quad y = 2\)
From (2):
\(x+4 = 5,\quad x = 1\)
So x = 1 and y = 2.