Set 14: Systems of Equations (Intermediate)

Choice C is correct. Choice C is the correct answer. To eliminate a variable, we need matching coefficients. Step 1: Multiply the second equation by 2: 2(x + y) = 2(6)$2x + 2 y = 12$$$ Step 2: Subtract from the first equation: (3 x + 2 y) - (2 x + 2 y) = 16 - 12x = 4 Step 3: Substitute $x = 4$ into the second equation: $$$4+ y = 6$y = 2 Solution: $(4, 2)$ Verification: $3(4) + 2(2) = 12 + 4 = 16$ ✓ Strategic Tip: Multiply equations to create matching or opposite coefficients for elimination. Choice A is incorrect because $3(3) + 2(3) = 9 + 6 = 15 \neq 16$. Choice B is incorrect because $3(5) + 2(1) = 15 + 2 = 17 \neq 16$. Choice D is incorrect because $3(2) + 2(4) = 6 + 8 = 14 \neq 16$.