Choice C is the correct answer. Let $x$ be the larger number and $y$ be the smaller number.

System: $\begin{cases} x + y = 30 \\ x - y = 12 \end{cases}$

Step 1: Add the equations to eliminate $y$: $2x = 42$$x = 21$

Step 2: Find $y$ using $x + y = 30$: $21 + y = 30$$y = 9$

Solution: The smaller number is 9.

Verification: $21 + 9 = 30$ ✓ and $21 - 9 = 12$ ✓

💡 Strategic Tip: Addition eliminates the variable with opposite signs.

Choice A is incorrect because if $y = 8$, then $x = 22$, and $22 - 8 = 14 \ eq 12$.

Choice B is incorrect because if $y = 10$, then $x = 20$, and $20 - 10 = 10 \ eq 12$.

Choice D is incorrect because this is the difference, not the smaller number.