Set 15: Systems of Equations (Advanced)

Choice D is correct. Choice D is the correct answer. The $y$ terms are opposites ($+y$ and $-y$), so we can add the equations to eliminate $y$. Step 1: Add the two equations: (4 x + y) + (4 x - y) = 18 + 10$8x = 28$x = \frac{28}{8} = \frac{7}{2} = 3.5 Step 2: Substitute $x = 3.5$ into the first equation: 4(3.5) + y = 18$14+ y = 18$y = 4 Solution: $(3.5, 4)$ Verification: $4(3.5) - 4 = 14 - 4 = 10$ ✓ Strategic Tip: Opposite coefficients make elimination by addition very efficient. Choice A is incorrect because $4(6) + (-6) = 24 - 6 = 18$ ✓, but $4(6) - (-6) = 24 + 6 = 30 \neq 10$. Choice B is incorrect because $4(4) + 2 = 16 + 2 = 18$ ✓, but $4(4) - 2 = 16 - 2 = 14 \neq 10$. Choice C is incorrect because $4(5) - (-2) = 20 + 2 = 22 \neq 10$.