1. **Stating the problem:** Solve the simultaneous equations for variables $x$ and $y$. 2. **General approach:** To solve simultaneous equations, we use substitution or elimination methods. The goal is to find values of $x$ and $y$ that satisfy both equations simultaneously. 3. **Example:** Suppose the system is: $$\begin{cases} 2x + 3y = 6 \\ 4x - y = 5 \end{cases}$$ 4. **Step 1: Solve one equation for one variable.** From the second equation: $$4x - y = 5 \implies y = 4x - 5$$ 5. **Step 2: Substitute into the first equation:** $$2x + 3(4x - 5) = 6$$ 6. **Step 3: Simplify and solve for $x$:** $$2x + 12x - 15 = 6$$ $$14x - 15 = 6$$ $$14x = 6 + 15$$ $$14x = 21$$ $$x = \frac{21}{14}$$ $$x = \frac{3}{2}$$ 7. **Step 4: Substitute $x$ back to find $y$:** $$y = 4\times \frac{3}{2} - 5$$ $$y = 6 - 5$$ $$y = 1$$ 8. **Final answer:** $$x = \frac{3}{2}, \quad y = 1$$ This method can be applied to any pair of simultaneous linear equations.