Set 13: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. The $y$ terms are opposites, so we add the equations. Step 1: Add the equations: (2 x + y) + (2 x - y) = 11 + 5$4x = 16$x = 4 Step 2: Substitute $x = 4$ into the first equation: 2(4) + y = 11$8+ y = 11$y = 3 Solution: $(4, 3)$ Verification: $2(4) - 3 = 8 - 3 = 5$ ✓ Strategic Tip: Elimination is fastest when coefficients already match or are opposites. Choice A is incorrect because $2(3) + 5 = 6 + 5 = 11$ ✓, but $2(3) - 5 = 6 - 5 = 1 \neq 5$. Choice B is incorrect because $2(5) - 1 = 10 - 1 = 9 \neq 5$. Choice D is incorrect because $2(2) + 7 = 4 + 7 = 11$ ✓, but $2(2) - 7 = 4 - 7 = -3 \neq 5$.