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Question 1 • CMS 2026-2027 NC Math 2 CREDIT RECOVERY

Which graph shows a system of equations with exactly one solution?

Answer

Image with description On a coordinate plane, two concentric circles has a center in the second quadrant. The smaller circle has a radius of 2 units, and the larger circle has a radius of 5 units.

Image with description On a coordinate plane, the circle is in the first quadrant with a radius of 3 units. The line passes through (0 comma 3) and (3 comma 0). The line does not intersect through the circle.

Image with description On a coordinate plane, the center of the circle lies in the third quadrant and has a radius of 3 units. The parabola opens downwards has a vertex in the first quadrant, and passes through the circle.

Image with description On a coordinate plane, the two parabolas have a common vertex. One of the parabola opens upwards, and the other opens downwards.

Explanation

The two parabolas in choice C share a vertex, and one opens upward while the other opens downward. Their graphs meet at that shared vertex; away from it, one lies above the vertex and the other lies below, so they have exactly one intersection. That single intersection represents exactly one solution to the system.

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