Set 6: Systems of Equations

Choice C is correct. Choice C is the correct answer. We use substitution since $y = 3 x - 2$ is already isolated. Step 1: Substitute $y = 3 x - 2$ into $x + y = 14$: x + (3 x - 2) = 14$4x - 2 = 144x = 16x = 4$$ Step 2: Find y$using$y = 3 x - 2: $$y = 3(4) - 2 = 12 - 2 = 10$$ Solution: (4, 10)$ Verification: $4+ 10 = 14$ ✓ Strategic Tip: When y is isolated, substitute directly into the other equation. Choice A is incorrect because $5+ 13 = 18 \neq 14$. Choice B is incorrect because $3+ 7 = 10 \neq 14$. Choice D is incorrect because $6+ 8 = 14$ ✓, but $8\neq 3(6) - 2 = 16$.