Set 2: Systems of Equations

Choice C is correct. Choice C is the correct answer. Let $x$ be the larger number and $y$ be the smaller number. System: $\begin{cases} x + y = 36 \\ x - y = 10 \end{cases}$ Step 1: Add the equations to eliminate $y$: 2x = 46$x = 23$$ Step 2: Find $y$ using $x + y = 36$: 23+ y = 36$y = 13$Solution: The larger number is 23. Verification:$23+ 13 = 36$✓ and$23- 13 = 10$✓ Strategic Tip: Addition is perfect for sum-and-difference problems. Choice A is incorrect because$20+ 16 = 36$✓, but$20- 16 = 4 \neq 10$. Choice B is incorrect because$24+ 12 = 36$✓, but$24- 12 = 12 \neq 10$. Choice D is incorrect because$26+ 10 = 36$✓, but$26- 10 = 16 \neq 10$$.