Systems of Inequalities Tutor Help
Stuck on systems of inequalities? Review the core ideas, read answers to common questions, and send a question to a tutor.
1 Quick recap
Inequalities shade regions: y > / ≥ shades above, y < / ≤ shades below. ≤/≥ give solid boundaries, </> dashed. A system’s solution is the overlap of the shadings; the vertex is where two boundaries cross.
Core ideas
- Sign direction decides the shaded side.
- Solid for ≤/≥, dashed for .
- Test (0, 0) when unsure of the side.
- System solution = overlap of shadings.
- Vertex = intersection of two boundaries.
2 Questions students ask
The questions a tutor hears most about this skill.
Read the inequality sign: y > … shades above, y < … shades below. When in doubt, test (0, 0) — if it satisfies the inequality, shade the side containing the origin.
A solid boundary means the points on the line count (≤, ≥); a dashed one means they do not (<, >). Mixing them up flips the answer at every boundary point.
Every point that satisfies ALL the inequalities at once — the overlap of the shadings. A point only needs to fail one inequality to be out.
3 Ask a tutor
Stuck on a problem? Send it in — a tutor will walk you through it.