A system of inequalities asks for a point that makes every condition true at once. Two inequalities followed by ordered-pair choices cue you to graph both in Desmos and plot the choices. The answer must land in both shaded regions, not just one. Watch the boundaries too: includes its line, while excludes its line.
Hints
- Hint 1
An ordered pair puts its first number on the horizontal axis and its second on the vertical axis. To satisfy both inequalities, where must its point sit?
- Hint 2
Each inequality shades the points that satisfy it. The overlap contains pairs that satisfy both, so a point in only one shaded region cannot solve the system. Plot the four choices to see where each lands.
Step-by-step
Graph the overlap in Desmos
Step 1Graph both solution regions
Type and on separate lines in Desmos. Each shaded solution region contains the points that satisfy its inequality, so the overlap contains points that satisfy both. The line counts; the line does not.
- Step 2
Plot the choices and find the overlap
Type each ordered pair on its own line, with the first number as and the second as . Only lands in both shadings; each other point misses at least one. So the ordered pair that solves the system is . Choice C.