1. **Problem Statement:** Solve the system of linear equations. Since you did not provide specific equations, I will explain the general method for solving linear systems. 2. **Formula and Rules:** A linear system can be written as: $$\begin{cases} a_1x + b_1y = c_1 \\ a_2x + b_2y = c_2 \end{cases}$$ where $a_1,b_1,c_1,a_2,b_2,c_2$ are constants. 3. **Methods to Solve:** - Substitution: Solve one equation for one variable and substitute into the other. - Elimination: Add or subtract equations to eliminate one variable. - Matrix method: Use matrices and inverse or row reduction. 4. **Example:** Solve $$\begin{cases} 2x + 3y = 6 \\ 4x - y = 5 \end{cases}$$ 5. **Step 1 (Elimination):** Multiply second equation by 3 to align $y$ coefficients: $$\begin{cases} 2x + 3y = 6 \\ 12x - 3y = 15 \end{cases}$$ 6. **Step 2:** Add equations to eliminate $y$: $$ (2x + 3y) + (12x - 3y) = 6 + 15 $$ $$ 2x + 12x + 3y - 3y = 21 $$ $$ 14x = 21 $$ 7. **Step 3:** Solve for $x$: $$ x = \frac{21}{14} $$ $$ x = \frac{3}{2} $$ 8. **Step 4:** Substitute $x=\frac{3}{2}$ into first equation: $$ 2\left(\frac{3}{2}\right) + 3y = 6 $$ $$ 3 + 3y = 6 $$ 9. **Step 5:** Solve for $y$: $$ 3y = 6 - 3 $$ $$ 3y = 3 $$ $$ y = 1 $$ 10. **Final Answer:** $$ \boxed{\left(\frac{3}{2}, 1\right)} $$ This is the solution to the system. If you have specific equations, please provide them for a detailed solution.