Apply Cramer's rule to solve a system of two linear equations, such as $\left\{\begin{array}{l} 3x + y = -3 \\ 2x + 3y = 6 \end{array}\right.$. First, evaluate the main determinant $D$ using the coefficients of the variables. Next, evaluate the determinants $D_x$ and $D_y$ by substituting the system's constants in place of the respective variable coefficients. Then, calculate the values of the variables using the formulas $x = \frac{D_x}{D}$ and $y = \frac{D_y}{D}$. Finally, state the solution as an ordered pair and verify it by substituting the values back into the original equations.