Choice C is the correct answer. To find the intersection, we set the two expressions for $y$ equal to each other.

Step 1: Set the equations equal: $-3x + 15 = 2x$

Step 2: Solve for $x$: $15 = 2x + 3x$$15 = 5x$$x = 3$

Step 3: Find $y$ using either equation (using the second): $y = 2(3) = 6$

Solution: $(3, 6)$

Verification: $6 = -3(3) + 15 = -9 + 15 = 6$ ✓

💡 Strategic Tip: The intersection is where both lines share the same point.

Choice A is incorrect because$8 = 2(4) = 8$ ✓, but $8 \ eq -3(4) + 15 = 3$.

Choice B is incorrect because$4 = 2(2) = 4$ ✓, but $4 \ eq -3(2) + 15 = 9$.

Choice D is incorrect because$10 = 2(5) = 10$ ✓, but $10 \ eq -3(5) + 15 = 0$.