Set 1: Systems of Equations (Intermediate)

Choice B is correct. Choice B is the correct answer. Multiply second equation by 3 and add to first. Step 1: Multiply second by 3: $6x - 3 y = 15$ Step 2: Add to first: (5 x + 3 y) + (6 x - 3 y) = 29 + 15$11x = 44$x = 4 Step 3: Substitute: $2(4) - y = 5 \Rightarrow y = 3$ Solution: $(4, 3)$ Verification: $5(4) + 3(3) = 29$ ✓ and $2(4) - 3 = 5$ ✓ Strategic Tip: Multiplying by 3 creates $-3 y$ to cancel $+3 y$. Choice A is incorrect because $2(7) - (-2) = 16 \neq 5$. Choice C is incorrect because $5(5) + 3(\frac{4}{3}) = 29$ ✓, but $2(5) - \frac{4}{3} \neq 5$. Choice D is incorrect because $5(3) + 3(\frac{14}{3}) = 29$ ✓, but $2(3) - \frac{14}{3} \neq 5$.