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 - 1$$3x = 6$$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$3 \ eq 2(1) + 1 = 3$ ✓, but $3 \ eq -1 + 7 = 6$.

Choice B is incorrect because$7 = 2(3) + 1 = 7$ ✓, but $7 \ eq -3 + 7 = 4$.

Choice D is incorrect because$3 \ eq 2(4) + 1 = 9$.