A system of inequalities asks for a point that makes every condition true. Graph each inequality as written in Desmos, then plot the proposed points and look for the overlap of the shaded regions. Watch the boundaries: a point on a dotted line is excluded, and a point that passes only one inequality is not a solution.
Hints
- Hint 1
Each inequality shades the points that satisfy it. In a system, you need the overlap, where both shadings cover the same point. Type the two inequalities on separate Desmos lines to see that region.
- Hint 2
Plot each ordered pair with its first number as and its second as . A point on the dotted boundary of makes the two sides equal, so it does not count.
Step-by-step
Graph the overlap and plot the choices
Step 1Show the points that satisfy both inequalities
Type and on separate Desmos lines. Each shades the points that satisfy it, so look for the overlap. The first boundary line is dotted because excludes equality; the second is solid because includes it.
- Step 2
Find and check the point in the overlap
Plot , , , and on separate Desmos lines. Only is in both shaded regions. The other points miss the second region; also touches the dotted first boundary, which doesn't count. To check , put the first coordinate in for and the second in for : . A solution to a system must pass every inequality. So solves the system. Choice C.