1. **State the problem:** Solve the system of equations using Cramer's rule. Suppose the system is: $$\begin{cases} a_1x + b_1y = c_1 \\ a_2x + b_2y = c_2 \end{cases}$$ 2. **Formula used:** Cramer's rule states that the solution $(x,y)$ is given by: $$x = \frac{\det(A_x)}{\det(A)}, \quad y = \frac{\det(A_y)}{\det(A)}$$ where $A$ is the coefficient matrix: $$A = \begin{bmatrix} a_1 & b_1 \\ a_2 & b_2 \end{bmatrix}$$ $A_x$ is obtained by replacing the first column of $A$ with the constants: $$A_x = \begin{bmatrix} c_1 & b_1 \\ c_2 & b_2 \end{bmatrix}$$ and $A_y$ is obtained by replacing the second column of $A$ with the constants: $$A_y = \begin{bmatrix} a_1 & c_1 \\ a_2 & c_2 \end{bmatrix}$$ 3. **Important rule:** If $\det(A) = 0$, the system has no unique solution. 4. **Calculate determinants:** $$\det(A) = a_1b_2 - a_2b_1$$ $$\det(A_x) = c_1b_2 - c_2b_1$$ $$\det(A_y) = a_1c_2 - a_2c_1$$ 5. **Find the solution:** $$x = \frac{c_1b_2 - c_2b_1}{a_1b_2 - a_2b_1}$$ $$y = \frac{a_1c_2 - a_2c_1}{a_1b_2 - a_2b_1}$$ This completes the solution using Cramer's rule. Note: Please provide the specific system of equations if you want the numerical solution.