Set 12: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. The $2y$ terms are opposites ($+2 y$ and $-2 y$), so we can add the equations to eliminate $y$. Step 1: Add the two equations: (5 x + 2 y) + (5 x - 2 y) = 23 + 17$10x = 40$x = 4 Step 2: Substitute $x = 4$ into the first equation: 5(4) + 2 y = 23$20+ 2 y = 232y = 3y = \frac{3}{2}$$ Solution: (4, \frac{3}{2})$Verification:$5(4) - 2(\frac{3}{2}) = 20 - 3 = 17$✓ Strategic Tip: Opposite coefficients signal that addition will eliminate the variable cleanly. Choice A is incorrect because$5(5) + 2(-1) = 25 - 2 = 23$✓, but$5(5) - 2(-1) = 25 + 2 = 27 \neq 17$. Choice B is incorrect because$5(3) + 2(4) = 15 + 8 = 23$✓, but$5(3) - 2(4) = 15 - 8 = 7 \neq 17$. Choice D is incorrect because$5(6) - 2(-\frac{7}{2}) = 30 + 7 = 37 \neq 17$.