1. **State the problem:** Solve the system of equations and confirm the solution by graphing. 2. **General approach:** To solve a system of equations, we find values of variables that satisfy all equations simultaneously. 3. **Assuming the system is:** $$\begin{cases} ax + by = c \\ dx + ey = f \end{cases}$$ 4. **Use substitution or elimination method:** 5. **Example:** Solve $$\begin{cases} 2x + 3y = 6 \\ x - y = 1 \end{cases}$$ 6. From the second equation, express $x$: $$x = y + 1$$ 7. Substitute into the first equation: $$2(y + 1) + 3y = 6$$ 8. Simplify: $$2y + 2 + 3y = 6$$ $$5y + 2 = 6$$ 9. Subtract 2 from both sides: $$5y + \cancel{2} - \cancel{2} = 6 - 2$$ $$5y = 4$$ 10. Divide both sides by 5: $$\frac{5y}{\cancel{5}} = \frac{4}{5}$$ $$y = \frac{4}{5}$$ 11. Substitute $y$ back to find $x$: $$x = \frac{4}{5} + 1 = \frac{4}{5} + \frac{5}{5} = \frac{9}{5}$$ 12. **Solution:** $$\boxed{\left( \frac{9}{5}, \frac{4}{5} \right)}$$ 13. **Confirm by graphing:** - Graph $y = \frac{6 - 2x}{3}$ from the first equation. - Graph $y = x - 1$ from the second equation. - The intersection point is at $\left( \frac{9}{5}, \frac{4}{5} \right)$ confirming the solution.