Question

Which graph shows a system of equations with no solutions? On a coordinate plane, the graphs of 2 circles are shown. Both circles have a center at (0, 0). The smaller circle is within the larger circle and the smaller circle has a radius that is 2 units smaller than the larger circle. On a coordinate plane, a graph of a line and a parabola are shown. The line is horizontal to the x-axis at y = negative 5. The parabola opens up and its vertex on the line. On a coordinate plane, the graphs of 2 circles are shown. Both circles are in quadrant 1, and they intersect each other. On a coordinate plane, the graphs of 2 parabolas are shown. Both parabolas open up and they intersect each other at (0, 0). The first parabola has a vertex in quadrant 3 and the second parabola has a vertex in quadrant 4.

Answer 1

Case 1: No solution

Explanation:

Case 1: On a coordinate plane, the graphs of 2 circles are shown. Both circles have a center at (0, 0). The smaller circle is within the larger circle and the smaller circle has a radius that is 2 units smaller than the larger circle. NO SOLUTION, SINCE THE GRAPHS NEVER INTERSECT.

Case 2: a graph of a line and a parabola are shown. The line is horizontal to the x-axis at y = negative 5. The parabola opens up and its vertex on the line. This system has two solutions, as the graphs intersect in two places.

Case 3: On a coordinate plane, the graphs of 2 parabolas are shown. Both parabolas open up and they intersect each other at (0, 0). The first parabola has a vertex in quadrant 3 and the second parabola has a vertex in quadrant 4. The graphs intersect at one point and thus this system has a solution.

Answer 2

1st Graph: 2 circles are shown

Explanation:

In order to have a solution set, the 2 graphs need to intersect each other. All the graphs but the 2 circles intersect and have a solution. Therefore, our answer is the 1st Graph.