A system of inequalities is a set of conditions that must all hold for the same point. When one coordinate is fixed, graph both inequalities in Desmos and draw a line through that coordinate. Plot the candidate points on the line and keep only those in the overlap. A point on a dotted boundary fails a strict inequality, even if it looks like it touches the shading.
Hints
- Hint 1
The second coordinate of is its -value, so every candidate lies on the horizontal line . Where does that line pass through both shaded regions?
- Hint 2
A system requires both inequalities to be true at once. Type each inequality on its own line in Desmos, then look for the part of inside both shadings.
- Hint 3
A strict inequality such as excludes points where the two sides are equal. A candidate on its dotted boundary doesn't count, even if it appears to touch the shading.
Step-by-step
Graph the overlap at the given height
Step 1Graph both conditions
Type and on separate Desmos lines. Desmos shades the points meeting each condition. Where the shadings overlap, both conditions hold; a point in only one shading won't work.
- Step 2
Locate points with the given coordinate
The second coordinate in is , so add . Desmos draws a horizontal line. Only the part inside both shadings can contain a solution. Along this line, the dotted edge is excluded, while the solid edge is included.
- Step 3
Plot the candidates
Type , , , and on separate lines. Desmos shows only in both shadings. It sits on the solid boundary, which counts because allows equality. The point sits on the dotted boundary and doesn't count. So could be . Choice C.