Set 11: Systems of Equations (Intermediate)

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: $4x + 2 = x + 11$ Step 2: Solve for $x$: $$$4x - x = 11 - 23x = 9$x = 3 Step 3: Find $y$ using either equation (using the second): $y = 3 + 11 = 14$ Solution: $(3, 14)$ Verification: $14= 4(3) + 2 = 12 + 2 = 14$ ✓ Strategic Tip: The intersection point is where both lines have the same coordinates. Choice A is incorrect because $10= 4(2) + 2 = 10$ ✓, but $10\neq 2 + 11 = 13$. Choice B is incorrect because $18= 4 + 11 = 15 \neq 18$. Choice D is incorrect because $12= 1 + 11 = 12$ ✓, but $12\neq 4(1) + 2 = 6$.