Set 12: Systems of Equations (Advanced)

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: (6 x + 2 y) + (6 x - 2 y) = 20 + 16$12x = 36$x = 3 Step 2: Substitute $x = 3$ into the first equation: 6(3) + 2 y = 20$18+ 2 y = 202y = 2y = 1$$ Solution: (3, 1)$Verification:$6(3) - 2(1) = 18 - 2 = 16$✓ Strategic Tip: Opposite coefficients make addition the fastest elimination method. Choice A is incorrect because$6(2) + 2(4) = 12 + 8 = 20$✓, but$6(2) - 2(4) = 12 - 8 = 4 \neq 16$. Choice B is incorrect because$6(4) - 2(-2) = 24 + 4 = 28 \neq 16$. Choice D is incorrect because$6(5) + 2(-5) = 30 - 10 = 20$✓, but$6(5) - 2(-5) = 30 + 10 = 40 \neq 16$.