1. **State the problem:** Determine if the two given systems of linear equations are equivalent and explain why graphing is preferred for systems of linear inequalities. 2. **Explain graphing preference:** Graphing a system of linear inequalities visually shows the solution region where all inequalities overlap, making it easier to understand the feasible solutions compared to algebraic methods. 3. **Analyze the first system:** $$\begin{cases} x + y = 10 \\ 2x - y = 4 \end{cases}$$ 4. **Analyze the second system:** $$\begin{cases} 2x + 2y = 20 \\ 2x - y = 4 \end{cases}$$ 5. **Check equivalence of first equations:** Multiply the first equation of the first system by 2: $$2(x + y) = 2 \times 10 \Rightarrow 2x + 2y = 20$$ This matches the first equation of the second system. 6. **Compare second equations:** Both systems have the same second equation: $$2x - y = 4$$ 7. **Conclusion on equivalence:** Since the second system's equations are just scalar multiples or identical to the first system's equations, the two systems are equivalent. 8. **Graph interpretation:** The first system's graph shows two lines intersecting near $(6, -6)$, indicating a unique solution. The second system's graph shows two parallel lines, which contradicts the algebraic equivalence, suggesting a possible error in the graph or interpretation. 9. **Final answer:** The two systems are algebraically equivalent because the second system's first equation is a multiple of the first system's first equation, and the second equations are identical. **Slug:** system equivalence **Subject:** algebra