Set 5: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. Let $x$ be the larger number and $y$ be the smaller number. System: $\begin{cases} x + y = 24 \\ x - y = 8 \end{cases}$ Step 1: Add the equations to eliminate $y$: 2x = 32$x = 16$$ Step 2: Find $y$ using $x + y = 24$: 16+ y = 24$y = 8$Solution: The larger number is 16. Verification:$16+ 8 = 24$✓ and$16- 8 = 8$✓ Strategic Tip: Sum and difference problems are perfect for elimination method. Choice A is incorrect because$14+ 10 = 24$✓, but$14- 10 = 4 \neq 8$. Choice B is incorrect because$18+ 6 = 24$✓, but$18- 6 = 12 \neq 8$$. Choice D is incorrect because this is the smaller number, not the larger one.