Set 16: Systems of Equations

Choice C is correct. Choice C is the correct answer. First, Step 1: Rearrange $y = 3 x - 5$ to standard form: $-3 x + y = -5$ or $3x - y = 5$ Step 2: Now we have: $\begin{cases} 3 x - y = 5 \\ 2 x + y = 15 \end{cases}$ The $y$ terms are opposites, so add: $$$5x = 20x = 4$$ Step 3: Substitute x = 4 into the second equation: $$2(4) + y = 158+ y = 15y = 7$$ Solution: (4, 7)Verification: $$7= 3(4) - 5 = 12 - 5 = 7$$ ✓ Strategic Tip: Converting to standard form(Ax + By = C)$often reveals elimination opportunities. Choice A is incorrect because$2(5) + 10 = 20 \neq 15$. Choice B is incorrect because$2(3) + 4 = 10 \neq 15$. Choice D is incorrect because$2(6) + 13 = 25 \neq 15$.