Systems of Inequalities
Solution region is the overlap of half-planes.
Key idea
Solution region is the overlap of half-planes.
In depth
Each inequality shades a half-plane; the solution is the overlap of all shaded regions. Use dashed lines for strict inequalities and solid for non-strict ones. Test a point to choose the side.
Worked example
y > x and y < 4 − x: the region above y = x and below y = 4 − x.
Real-world uses
- Finding feasible production plans that meet time and material limits in a small factory
Common mistake
Shading the wrong side. Always test a point like (0, 0).
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Systems of Inequalities?
Solution region is the overlap of half-planes. It is a topic at the advanced level in Algebra.
Where is Systems of Inequalities used in real life?
Real-world examples: Finding feasible production plans that meet time and material limits in a small factory.
What should I learn before Systems of Inequalities?
Make sure you are comfortable with Systems with Three Variables, the previous topic in Algebra.
What is a common mistake with Systems of Inequalities?
Shading the wrong side. Always test a point like (0, 0).
How can I practise Systems of Inequalities?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Systems of Inequalities?
Move on to Linear Programming next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.
- Quadratic Formula – Gives roots of any quadratic.