Set 12: Systems of Equations (Intermediate)

Choice C is correct. Choice C is the correct answer. The $3y$ terms are opposites, so we add the equations. Step 1: Add the equations: (5 x + 3 y) + (5 x - 3 y) = 29 + 11$10x = 40$x = 4 Step 2: Substitute $x = 4$ into the first equation: 5(4) + 3 y = 29$20+ 3 y = 293y = 9y = 3$$ Solution: (4, 3)$Verification:$5(4) - 3(3) = 20 - 9 = 11$✓ Strategic Tip: Opposite coefficients signal that addition will eliminate the variable. Choice A is incorrect because$5(3) + 3(\frac{14}{3}) = 15 + 14 = 29$✓, but$5(3) - 14 = 1 \neq 11$. Choice B is incorrect because$5(5) - 3(\frac{4}{3}) = 25 - 4 = 21 \neq 11$. Choice D is incorrect because$5(2) + 3(\frac{19}{3}) = 10 + 19 = 29$✓, but$5(2) - 19 = -9 \neq 11$.