Which of the following ordered pairs satisfies the system of inequalities above?
A system of inequalities asks for a pair that makes every condition true, not merely one. With several ordered-pair choices, graph each inequality in Desmos and plot the choices. Look for the overlapping shading, but check the boundary: a point on a dotted line is excluded even if it looks close to the shaded region.
Hints
- Hint 1
An inequality shades the points that make it true. Graph the first condition as written. Its strict sign makes the boundary dotted, so a point on that line doesn't count.
- Hint 2
A system means both conditions must hold at once. Add the second inequality and find where both shadings overlap. A point in only one shaded region won't work.
- Hint 3
In an ordered pair , the first number is and the second is . Plot the choices as points. Is any point on a dotted boundary rather than inside the overlap?
Step-by-step
Graph the overlap and plot the choices
Step 1Graph the first condition
Type into Desmos. It shades the points that make this inequality true. The dotted boundary is excluded because means greater than, not equal to.
- Step 2
Find where both conditions hold
Add . Desmos shows a second shaded region with a solid boundary: allows equality. Only points in both shadings satisfy the system.
- Step 3
Plot the choices in the overlap
Type each ordered pair on its own line. Desmos shows one point in both shadings: . The point sits on the dotted line, so it doesn't count. The pair satisfying the system is . Choice D.