Set 13: 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: $2x + 1 = -x + 7$ Step 2: Solve for $x$: $$$2x + x = 7 - 13x = 6$x = 2 Step 3: Find $y$ using either equation (using the first): $y = 2(2) + 1 = 4 + 1 = 5$ Solution: $(2, 5)$ Verification: $5= -2 + 7 = 5$ ✓ Strategic Tip: The intersection point of two lines is where their $y$-values are equal for the same $x$-value. Choice A is incorrect because $3\neq 2(1) + 1 = 3$ ✓, but $3\neq -1 + 7 = 6$. Choice B is incorrect because $7= 2(3) + 1 = 7$ ✓, but $7\neq -3 + 7 = 4$. Choice D is incorrect because $3\neq 2(4) + 1 = 9$.