Choice C is the correct answer. First, let's rearrange the first equation to standard form.

Step 1: Rearrange $y = 3x - 5$ to standard form: $-3x + y = -5$ or $3x - y = 5$

Step 2: Now we have: $\begin{cases} 3x - y = 5 \\ 2x + y = 15 \end{cases}$

The $y$ terms are opposites, so add: $5x = 20$$x = 4$

Step 3: Substitute $x = 4$ into the second equation: $2(4) + y = 15$$8 + y = 15$$y = 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$2(5) + 10 = 20 \ eq 15$.

Choice B is incorrect because$2(3) + 4 = 10 \ eq 15$.

Choice D is incorrect because$2(6) + 13 = 25 \ eq 15$.