Set 14: Systems of Equations (Intermediate)

Choice B is correct. Choice B is the correct answer. Let $g$ = goats and $d$ = ducks. System: $\begin{cases} g + d = 45 \\ 4 g + 2 d = 126 \end{cases}$ Step 1: From first: $d = 45 - g$ Step 2: Substitute: $$$4g + 2(45 - g) = 126$4g + 90 - 2 g = 126$2g = 36g = 18$$ Solution: 18 goats Verification: $$18+ 27 = 45$$ ✓ and 4(18) + 2(27) = 72 + 54 = 126$ ✓ Strategic Tip: Animals/legs problems are classic systems applications. Other choices fail verification.