Set 17: 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: $\begin{cases} x + y = 30 \\ x - y = 12 \end{cases}$ Step 1: Add the equations to eliminate $y$: 2x = 42$x = 21$$ Step 2: Find $y$ using $x + y = 30$: 21+ y = 30y = 9$$ 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 $$22- 8 = 14 \neq 12$$. Choice B is incorrect because if y = 10$, then$x = 20$, and $20- 10 = 10 \neq 12$. Choice D is incorrect because this is the difference, not the smaller number.