A system of inequalities asks for a point that makes every condition true. Graph each inequality in Desmos, then plot the offered pairs and look for the overlapping shading. Check any point on a boundary carefully: a strict sign excludes equality, while a sign with an equality bar includes it.
Hints
- Hint 1
A boundary line is where the two sides of an inequality are equal. A strict sign such as leaves that line out; includes its line. What does Desmos show when you graph each inequality?
- Hint 2
An ordered pair gives the horizontal coordinate first and the vertical coordinate second. Plot the choices and look for a point in both shaded regions. If one touches a boundary, check whether that boundary is included.
Step-by-step
Graph the overlap in Desmos
Step 1Graph the strict inequality
Type in Desmos. It shades points above its boundary line , where the two sides are equal. The line is dashed because does not allow equality.
- Step 2
Find where both shadings overlap
Add . Desmos shades points on or below its solid boundary line; solid means equality is allowed. A system needs both inequalities true at once. So only the overlapping shading can contain an answer.
- Step 3
Plot the choices and read the overlap
Type each offered pair as a point. touches the dashed, excluded boundary; misses the first shading, and misses the second. Only lies in the overlap, so it satisfies both inequalities. Choice C.