Set 9: Systems of Equations

Choice D is correct. Choice D is the correct answer. The $5y$ terms are opposites, so we add the equations. Step 1: Add the equations: (2 x + 5 y) + (2 x - 5 y) = 29 + 11$4x = 40$x = 10 Step 2: Substitute $x = 10$ into the first equation: 2(10) + 5 y = 29$20+ 5 y = 295y = 9y = \frac{9}{5}$$ Solution: (10, \frac{9}{5})$Verification:$2(10) - 5(\frac{9}{5}) = 20 - 9 = 11$✓ Strategic Tip: Fractional answers appear frequently on standardized tests. Choice A is incorrect because$2(9) + 5(\frac{11}{5}) = 18 + 11 = 29$✓, but$2(9) - 11 = 7 \neq 11$. Choice B is incorrect because$2(12) + 5(1) = 24 + 5 = 29$✓, but$2(12) - 5(1) = 19 \neq 11$. Choice C is incorrect because$2(7) + 5(3) = 14 + 15 = 29$✓, but$2(7) - 5(3) = 14 - 15 = -1 \neq 11$.