Cramer's rule

Determinant.
$$\det A = \begin{vmatrix} 2 & 1 \\ 1 & 3 \end{vmatrix} = 6 - 1 = 5.$$

Determinants $A_1$ and $A_2$.
$$\det A_1 = \begin{vmatrix} 5 & 1 \\ 10 & 3 \end{vmatrix} = 15 - 10 = 5, \qquad \det A_2 = \begin{vmatrix} 2 & 5 \\ 1 & 10 \end{vmatrix} = 20 - 5 = 15.$$

Solution.
$$x = \frac{\det A_1}{\det A} = \frac{5}{5} = 1, \qquad y = \frac{\det A_2}{\det A} = \frac{15}{5} = 3.$$

Verification. $2\cdot1+3=5$ and $1+3\cdot3=10$. Correct.