Question

Which statement about the following system of inequalities is true?

mc025-1.jpg
There is no solution because the shading does not overlap.
There is no solution because the graphs do not intersect.
The solution contains points in four quadrants of the coordinate plane.
The solution is equal to the solution to mc025-2.jpg.

Answer 1

I can't see the images mc025-1.jpg or mc025-2.jpg you mention. Could you either upload those images here or type the two inequalities / shaded regions exactly as shown?

If you want to check it yourself, here are quick steps to decide which statement is true:

1. Identify each boundary (turn each inequality into an equality). That gives lines/circles/etc.
2. Sketch each boundary and determine which side is shaded by testing a single point (usually (0,0) if it's not on a boundary).
3. The solution to the system is the intersection of the shaded regions:
- If the shaded regions do not overlap at all, the correct choice is “There is no solution because the shading does not overlap.”
- “There is no solution because the graphs do not intersect” is misleading: the boundary graphs might intersect but the shaded halves still may not overlap. Use this only if the boundaries and shaded halves produce no common points.
4. If there is an overlap, check whether that overlapping region reaches into each quadrant (test sample points with positive/negative x and y).
5. To decide whether the solution equals the solution to mc025-2.jpg, compare the two overlapping regions pointwise — they must coincide exactly.

Send the images or the exact inequalities and I’ll determine the correct choice and show the reasoning.