Set 3: Systems of Equations

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: (3 x + y) + (3 x - y) = 13 + 5$6x = 18$x = 3 Step 2: Substitute $x = 3$ into the first equation: 3(3) + y = 13$9+ y = 13$y = 4 Solution: $(3, 4)$ Verification: $3(3) - 4 = 9 - 4 = 5$ ✓ Strategic Tip: When coefficients are opposites, adding eliminates that variable immediately. Choice A is incorrect because $3(2) + 7 = 6 + 7 = 13$ ✓, but $3(2) - 7 = 6 - 7 = -1 \neq 5$. Choice B is incorrect because $3(4) - 1 = 12 - 1 = 11 \neq 5$. Choice D is incorrect because $3(5) - (-2) = 15 + 2 = 17 \neq 5$.