Set 2: Systems of Equations (Advanced)

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: (2 x + 3 y) + (2 x - 3 y) = 17 + 7$4x = 24$x = 6 Step 2: Substitute $x = 6$ into the first equation: 2(6) + 3 y = 17$12+ 3 y = 173y = 5y = \frac{5}{3}$$ Solution: (6, \frac{5}{3})$Verification:$2(6) - 3(\frac{5}{3}) = 12 - 5 = 7$✓ Strategic Tip: Don't be afraid of fractional answers—they're common on the SAT. Choice A is incorrect because$2(5) + 3(\frac{7}{3}) = 10 + 7 = 17$✓, but$2(5) - 3(\frac{7}{3}) = 10 - 7 = 3 \neq 7$. Choice B is incorrect because$2(7) + 3(1) = 14 + 3 = 17$✓, but$2(7) - 3(1) = 14 - 3 = 11 \neq 7$. Choice D is incorrect because$2(4) + 3(3) = 8 + 9 = 17$✓, but$2(4) - 3(3) = 8 - 9 = -1 \neq 7$.