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$9 - 9 = 0 \ eq 4$.

Choice B is incorrect because$12 + 6 = 18$ ✓, but $12 - 6 = 6 \ eq 4$.

Choice D is incorrect because$10 + 8 = 18$ ✓, but $10 - 8 = 2 \ eq 4$.