Find the values of x and y if $\begin{bmatrix$}[r] 2x + y \ 3x - 2y \end{bmatrix} = \begin{bmatrix} 5 \ 4 \end{bmatrix}.

Given $\begin{bmatrix$}[r] 2x + y \ 3x - 2y \end{bmatrix} = \begin{bmatrix} 5 \ 4 \end{bmatrix}.

By definition of equality of matrices, we get

2x + y = 5    [….Eq 1]
3x - 2y = 4    [….Eq 2]

2x + y = 5
⇒ y = 5 - 2x

Putting value of y in Eq 2,

3x - 2(5 - 2x) = 4
⇒ 3x - 10 + 4x = 4
⇒ 7x = 14
⇒ x = 2.

∴ x = 2, y = 5 - 2x = 5 - 4 = 1.

Hence, the value of x = 2 and y = 1.