Step 1

$ \Delta = \begin{vmatrix} 3 & 2 \\ 1 & 3 \end{vmatrix} = 9-2=7 \neq 0. \therefore $ Cramer's rule can be used.

Step 2

$\Delta x = \begin{vmatrix} 5 & 2 \\ 4 & 3 \end{vmatrix}=15-8=7$

$ \Delta y = \begin{vmatrix} 3 & 5 \\ 1 & 4 \end{vmatrix}=12-5=7$

Step 3

$ x = \large\frac{\Delta x}{\Delta} = \large\frac{7}{7}=1\: \: \: y = \large\frac{\Delta y}{\Delta} = \large\frac{7}{7}=1$

$(x,y) = (1,1)$