\(\begin{bmatrix}2x+1 & 4x\\ y+3 & 2y-5\end{bmatrix}=\begin{bmatrix}x+2 & 4\\ 7 & 3\end{bmatrix}\)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(x=1, y=4\)
Two matrices are equal only when their corresponding entries are equal. The options give x and y, so these are found from the entries.
First row, second column:
\(4x = 4\)
\(x = 1\)
Second row, first column:
\(y + 3 = 7\)
\(y = 4\)
The other two entries agree with these values:
\(2x + 1 = 3 = x + 2\)
\(2y - 5 = 3\)
So x = 1 and y = 4.