Set 5: Systems of Equations

Choice C is correct. Choice C is the correct answer. We use substitution since $y = 2 x + 5$ is already isolated. Step 1: Substitute $y = 2 x + 5$ into $3x - y = 1$: $$$3x - (2 x + 5) = 13x - 2 x - 5 = 1$x - 5 = 1x = 6 Step 2: Find $y$ using $y = 2 x + 5$: $y = 2(6) + 5 = 12 + 5 = 17$ Solution: $(6, 17)$ Verification: $3(6) - 17 = 18 - 17 = 1$ ✓ Strategic Tip: When one equation is solved for y, substitute into the other equation. Choice A is incorrect because $3(8) - 21 = 24 - 21 = 3 \neq 1$. Choice B is incorrect because $3(4) - 13 = 12 - 13 = -1 \neq 1$. Choice D is incorrect because $3(5) - 15 = 15 - 15 = 0 \neq 1$.