Set 1: Systems of Equations

Choice C is correct. Choice C is the correct answer. The $2y$ terms are opposites, so we add the equations. Step 1: Add the equations: (3 x + 2 y) + (3 x - 2 y) = 16 + 8$6x = 24$x = 4 Step 2: Substitute $x = 4$ into the first equation: 3(4) + 2 y = 16$12+ 2 y = 162y = 4y = 2$$ Solution: (4, 2)$Verification:$3(4) - 2(2) = 12 - 4 = 8$✓ Strategic Tip: Opposite coefficients signal that addition is the right move. Choice A is incorrect because$3(3) + 2(3.5) = 9 + 7 = 16$✓, but$3(3) - 2(3.5) = 9 - 7 = 2 \neq 8$. Choice B is incorrect because$3(5) - 2(0.5) = 15 - 1 = 14 \neq 8$. Choice D is incorrect because$3(2) + 2(5) = 6 + 10 = 16$✓, but$3(2) - 2(5) = 6 - 10 = -4 \neq 8$.