Set 14: Systems of Equations

Choice D is correct. Choice D is the correct answer. The $4y$ terms are opposites, so we add the equations. Step 1: Add the equations: (3 x + 4 y) + (3 x - 4 y) = 25 + 11$6x = 36$x = 6 Step 2: Substitute $x = 6$ into the first equation: 3(6) + 4 y = 25$18+ 4 y = 254y = 7y = \frac{7}{4}$$ Solution: (6, \frac{7}{4})$Verification:$3(6) - 4(\frac{7}{4}) = 18 - 7 = 11$✓ Strategic Tip: Don't avoid fractional answers—they're common on the SAT. Choice A is incorrect because$3(5) + 4(2.5) = 15 + 10 = 25$✓, but$3(5) - 4(2.5) = 15 - 10 = 5 \neq 11$. Choice B is incorrect because$3(7) + 4(1) = 21 + 4 = 25$✓, but$3(7) - 4(1) = 21 - 4 = 17 \neq 11$. Choice C is incorrect because$3(4) + 4(3.25) = 12 + 13 = 25$✓, but$3(4) - 13 = -1 \neq 11$.