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. System: $\begin{cases} x + y = 18 \\ x - y = 4 \end{cases}$ Step 1: Add the equations to eliminate $y$: 2x = 22$x = 11$$ Step 2: Find $y$ using $x + y = 18$: 11+ y = 18$y = 7$Solution: The numbers are 11 and 7. Verification:$11+ 7 = 18$✓ and$11- 7 = 4$✓ Strategic Tip: Sum and difference problems are ideal for the elimination method. Choice A is incorrect because$9- 9 = 0 \neq 4$. Choice B is incorrect because$12+ 6 = 18$✓, but$12- 6 = 6 \neq 4$. Choice D is incorrect because$10+ 8 = 18$✓, but$10- 8 = 2 \neq 4$$.