1. **State the problem:** Solve the simultaneous equations for variables $x$ and $y$. 2. **General approach:** Simultaneous equations are solved by either substitution or elimination methods. 3. **Example:** Suppose the system is: $$\begin{cases} ax + by = c \\ dx + ey = f \end{cases}$$ 4. **Substitution method:** Solve one equation for one variable, then substitute into the other. 5. **Elimination method:** Multiply equations to align coefficients, then add or subtract to eliminate one variable. 6. **Intermediate step example:** If eliminating $y$, multiply first equation by $e$ and second by $b$: $$\begin{cases} e(ax + by) = ec \\ b(dx + ey) = bf \end{cases}$$ which is $$\begin{cases} eax + eby = ec \\ bdx + bey = bf \end{cases}$$ 7. **Subtract equations to eliminate $y$:** $$eax + \cancel{eby} - bdx - \cancel{bey} = ec - bf$$ 8. **Simplify:** $$ (ea - bd)x = ec - bf $$ 9. **Solve for $x$:** $$ x = \frac{ec - bf}{ea - bd} $$ 10. **Substitute $x$ back into one original equation to find $y$:** $$ ax + by = c \Rightarrow by = c - ax \Rightarrow y = \frac{c - a x}{b} $$ 11. **Summary:** Use substitution or elimination to find $x$ and $y$ by isolating variables and simplifying. This method works for any linear simultaneous equations with two variables.