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Question 6 • CMS 2026-2027 NC Math 2 CREDIT RECOVERY

Which graph shows a system of equations with no solutions?

Answer

Image with description On a coordinate plane, the line is parallel to the x axis and passes through (0 comma negative 5). The parabola opens upwards, and it touches the line at its vertex.

Image with description On a coordinate plane, two concentric circles have a center at the origin. The smaller circle has a radius of 2 units smaller than the larger circle.

Image with description On a coordinate plane, two circles are intersecting each other in the first quadrant.

Image with description On a coordinate plane, the two parabolas open up and intersect each other at the origin. The first parabola has a vertex in the third quadrant, and the second parabola has a vertex in the fourth quadrant.

Explanation

A solution to a system shown on a graph is a point where the graphs intersect. In choice B, the circles have the same center but different radii, so one lies entirely inside the other and they never intersect. The other choices show graphs that intersect at least once, so they have solutions.

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