Question

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(4 points)
Use the Systems of Inequalities graphed below to answer the questions.



What is the inequality symbol of the green line?

What is the inequality symbol of the purple line?

Is the point (-3, -5) a solution to the system of inequalities?

Is the point (1, 6) a solution to the system of inequalities?

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Answer 1

I don’t have the graph image, so I can’t read the line types or the shaded regions. Please either upload the graph or describe for each colored line: (a) whether the line is solid or dashed and (b) which side is shaded (above the line or below the line). With that I’ll give the exact inequality symbols and check the two points.

If you want to decide now, here are the rules you can use:

- Solid line means ≤ or ≥ (inclusive). Dashed line means < or > (not inclusive).
- If the shaded region is above the line, use ≥ or >. If the shaded region is below the line, use ≤ or <.
(More precisely: write the line as y = mx + b. If shading is the region where y is larger than the line, use > or ≥; if shading is where y is smaller than the line, use < or ≤.)
- To test a point (x, y) for the system, substitute into both inequalities. The point is a solution only if it satisfies both.

Example: if a green line is solid and shaded below and its equation is y = 2x + 1, the green inequality is y ≤ 2x + 1. To test (-3, -5) you check -5 ≤ 2(−3)+1 → -5 ≤ -5 (true). Then check the purple inequality similarly.

Send the graph (or the two line equations plus whether each shading is above/below and whether each line is solid/dashed) and I’ll answer the four questions precisely.