A system of inequalities asks for a point that meets every condition. Graph both inequalities in Desmos, then plot the answer choices and look for a point in the overlap of the shaded regions. Check any point that touches a line: a solid boundary counts, but a dashed boundary doesn't.
Hints
- Hint 1
A boundary line is where the two sides of an inequality are equal. The sign allows points on its boundary, while does not. Which of the two lines should be solid?
- Hint 2
The solution set contains points that satisfy both inequalities. Type each inequality into Desmos on its own line and look for the overlapping shading. Then plot the choices to see which point belongs there.
Step-by-step
Graph the overlap in Desmos
Step 1Identify which boundaries count
Replace each inequality sign with to find its boundary line: and . The first line is included because allows equality. The second is dashed and excluded because does not.
- Step 2
Find the shaded overlap
Type and on separate Desmos lines. Desmos shades the points that satisfy each one. The overlap is the solution set, where a point satisfies both at once.
- Step 3
Plot the choices and read the result
Type the four answer choices as points. Desmos shows on the solid lower boundary and below the dashed upper boundary, so it counts. Each other point misses at least one shaded region. The point in the solution set is . Choice B.