Set 10: Systems of Equations (Intermediate)

Choice C is correct. Choice C 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: (x + y) + (x - y) = 7 + 3$2x = 10$x = 5 Step 2: Substitute $x = 5$ into the first equation: $$$5+ y = 7y = 2$$ Solution: (5, 2)Verification: $$5+ 2 = 7$$ ✓ and $$5- 2 = 3$$ ✓ Strategic Tip: When coefficients of a variable are opposites, adding the equations eliminates that variable immediately. Choice A is incorrect because $$4- 3 = 1 \neq 3$$. Choice B is incorrect because $$6+ 1 = 7$$ ✓, but $$6- 1 = 5 \neq 3$$. Choice D is incorrect because this swaps thex$and$y$ values from the correct answer.