1. **State the problem:** Solve the simultaneous equations for the variables involved. 2. **General approach:** To solve simultaneous equations, we use substitution or elimination methods. 3. **Example:** Suppose the system is: $$\begin{cases} ax + by = c \\ dx + ey = f \end{cases}$$ 4. **Step 1: Solve one equation for one variable.** For example, solve the first equation for $x$: $$x = \frac{c - by}{a}$$ 5. **Step 2: Substitute into the second equation:** $$d\left(\frac{c - by}{a}\right) + ey = f$$ 6. **Step 3: Multiply both sides by $a$ to clear the denominator:** $$\cancel{a} \cdot d \left(\frac{c - by}{\cancel{a}}\right) + aey = af$$ $$dc - dby + aey = af$$ 7. **Step 4: Group terms with $y$ and solve for $y$:** $$(-db + ae) y = af - dc$$ $$y = \frac{af - dc}{-db + ae}$$ 8. **Step 5: Substitute $y$ back into the expression for $x$:** $$x = \frac{c - b \left(\frac{af - dc}{-db + ae}\right)}{a}$$ 9. **Step 6: Simplify the expression for $x$ to find its value.** This method applies to any two linear simultaneous equations. **Final answer:** The solution $(x,y)$ is given by $$x = \frac{c - b \left(\frac{af - dc}{-db + ae}\right)}{a}, \quad y = \frac{af - dc}{-db + ae}$$