1. The problem is to solve a system of linear equations using the Vienna method (also known as Cramer's rule). 2. The Vienna method uses determinants to find the solution of a system of linear equations: $$Ax = b$$ where $A$ is the coefficient matrix, $x$ is the vector of variables, and $b$ is the constants vector. 3. The solution for each variable $x_i$ is given by: $$x_i = \frac{\det(A_i)}{\det(A)}$$ where $A_i$ is the matrix formed by replacing the $i$-th column of $A$ with the vector $b$. 4. Important rules: - $\det(A)$ must not be zero; otherwise, the system has no unique solution. - Calculate determinants carefully. 5. To apply the Vienna method, first write down the system of equations explicitly. 6. Then form matrix $A$ and vector $b$. 7. Calculate $\det(A)$. 8. For each variable, form $A_i$ by replacing the $i$-th column of $A$ with $b$ and calculate $\det(A_i)$. 9. Finally, compute each variable $x_i$ using the formula above. Since the user did not provide a specific system, this is the general method to use the Vienna method (Cramer's rule). Please provide the system of equations for a detailed solution.