Set 6: Systems of Equations

Choice C is correct. 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: $-3 x + 15 = 2 x$ Step 2: Solve for $x$: $$$15= 2 x + 3 x15= 5 x$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 $8\neq -3(4) + 15 = 3$. Choice B is incorrect because $4= 2(2) = 4$ ✓, but $4\neq -3(2) + 15 = 9$. Choice D is incorrect because $10= 2(5) = 10$ ✓, but $10\neq -3(5) + 15 = 0$.