Set 17: 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: $3x - 4 = -2 x + 6$ Step 2: Solve for $x$: $$$3x + 2 x = 6 + 45x = 10$x = 2 Step 3: Find $y$ using either equation (using the first): $y = 3(2) - 4 = 6 - 4 = 2$ Solution: $(2, 2)$ Verification: $2= -2(2) + 6 = -4 + 6 = 2$ ✓ Strategic Tip: The intersection point is where both lines have the same $x$ and $y$ values. Choice A is incorrect because $5= 3(3) - 4 = 9 - 4 = 5$ ✓, but $5\neq -2(3) + 6 = 0$. Choice B is incorrect because $-1 = 3(1) - 4 = -1$ ✓, but $-1 \neq -2(1) + 6 = 4$. Choice D is incorrect because $8= 3(4) - 4 = 8$ ✓, but $8\neq -2(4) + 6 = -2$.