Set 12: Systems of Equations

Choice D is correct. Choice D is the correct answer. Multiply first by 2 and add to second. Step 1: Multiply first by 2: $2x + 2 y = 18$ Step 2: Add to second: (2 x + 2 y) + (3 x - 2 y) = 18 + 7$5x = 25$x = 5 Step 3: Substitute: $5+ y = 9 \Rightarrow y = 4$ Solution: $(5, 4)$ Verification: $3(5) - 2(4) = 15 - 8 = 7$ ✓ Strategic Tip: Multiplying by 2 creates $+2 y$ to cancel $-2 y$. Choice A is incorrect because $3(6) - 2(3) = 12 \neq 7$. Choice B is incorrect because $3(4) - 2(5) = 2 \neq 7$. Choice C is incorrect because $3(7) - 2(2) = 17 \neq 7$.