1. The problem involves solving a system of 3 linear equations with 3 variables using Cramer's rule. 2. Cramer's rule states that for a system: $$\begin{cases}a_1x + b_1y + c_1z = d_1\\a_2x + b_2y + c_2z = d_2\\a_3x + b_3y + c_3z = d_3\end{cases}$$ we find the determinant of the coefficient matrix: $$D = \begin{vmatrix}a_1 & b_1 & c_1\\a_2 & b_2 & c_2\\a_3 & b_3 & c_3\end{vmatrix}$$ 3. Then find determinants replacing columns of the coefficient matrix by the constants vector: - For $x$: $$D_x = \begin{vmatrix}d_1 & b_1 & c_1\\d_2 & b_2 & c_2\\d_3 & b_3 & c_3\end{vmatrix}$$ - For $y$: $$D_y = \begin{vmatrix}a_1 & d_1 & c_1\\a_2 & d_2 & c_2\\a_3 & d_3 & c_3\end{vmatrix}$$ - For $z$: $$D_z = \begin{vmatrix}a_1 & b_1 & d_1\\a_2 & b_2 & d_2\\a_3 & b_3 & d_3\end{vmatrix}$$ 4. The solutions for variables are given by: $$x = \frac{D_x}{D},\quad y = \frac{D_y}{D},\quad z = \frac{D_z}{D}$$ 5. This method only works if $D \neq 0$. This completes the explanation of Cramer's rule for solving 3 equations with 3 unknowns.