Set 16: Systems of Equations (Intermediate)

Choice C is correct. Choice C is the correct answer. Let $x$ be the larger number and $y$ be the smaller number. We can set up a system of equations. System: $\begin{cases} x + y = 15 \\ x - y = 5 \end{cases}$ Step 1: Add the equations to eliminate $y$: 2x = 20$x = 10$$ Step 2: Substitute $x = 10$ into $x + y = 15$: 10+ y = 15$y = 5$Solution: The numbers are 10 and 5. Verification:$10+ 5 = 15$✓ and$10- 5 = 5$✓ Strategic Tip: Word problems involving "sum" and "difference" naturally lead to systems with opposites. Choice A is incorrect because$8+ 7 = 15$✓, but$8- 7 = 1 \neq 5$. Choice B is incorrect because$12- 3 = 9 \neq 5$. Choice D is incorrect because$9+ 6 = 15$✓, but$9- 6 = 3 \neq 5$$.