A system of inequalities asks for points that satisfy every rule at once. Graph both inequalities in Desmos, then check whether each table’s points lie in the overlapping shaded region. A point on a boundary can be a trap: excludes equality, while includes it.
Hints
- Hint 1
A system of inequalities requires each point to satisfy both rules. On a graph, look for the region shaded by both inequalities, not a region shaded by only one.
- Hint 2
The boundary line for is dashed because equality is excluded. What happens to a point that sits exactly on that line?
- Hint 3
An ordered pair gives first and second. You can eliminate a whole table as soon as you find one pair in it that fails either inequality.
Step-by-step
Graph the overlap and test the tables
Step 1Graph both conditions
Type and on separate Desmos lines. The overlap of their shadings contains points that satisfy both inequalities. Desmos draws the boundary dashed because equality is excluded, and the boundary solid because equality counts.
- Step 2
Eliminate tables with a failing pair
Plot , , and on separate lines. Desmos places and on the dashed lower boundary, so neither counts. It places above the solid upper boundary. One failing pair rules out its whole table.
- Step 3
Check every pair in the remaining table
Add , , and . Desmos places the first two inside the overlap. It places on the solid upper boundary and above the dashed lower boundary, so that point counts too. All three pairs satisfy both inequalities, so the table listing them works. Choice C.