Solve one-variable linear and compound inequalities using equivalent operations, reversing the inequality when multiplying or dividing by a negative, and represent solutions with number lines, intervals, or set notation. Solve two-variable systems of linear equations algebraically and graphically, including systems with unique, no, or infinitely many solutions, and solve linear–quadratic systems by substitution or graphing to identify zero, one, or two real intersection points. Graph linear inequalities and systems as half-planes with correctly included or excluded boundaries, interpret their intersections as feasible regions and solution sets, and use ordered pairs, units, and relevant corner points to assess feasible choices.
On this page:
- Master skills like “Interpret feasible regions in context”, “Solve linear inequalities in one variable”, and “Graph linear inequalities in two variables” with unlimited, free practice problems
- Download (or modify) free worksheets on Systems and Inequalities you can use at home or in class with practice problems across all skills in this group including “Solve systems of linear equations graphically”, “Interpret intersections as solutions to systems”, “Solve systems of linear equations algebraically”.
- Start working on adaptive units like “Linear Inequalities and Graphing - Intro” or “Algebra - Systems of Equations - Practice” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Systems and Inequalities: Individual Skills
Master 7 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
- Graph linear inequalities in two variables
- Interpret feasible regions in context
- Interpret intersections as solutions to systems
- Solve linear inequalities in one variable
- Solve systems of linear equations algebraically
- Solve systems of linear equations graphically
- Solve systems of linear inequalities graphically
Practice 'Graph linear inequalities in two variables'
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Download/Modify Free Grade 11 'Systems and Inequalities' Worksheet
Print this free 'Systems and Inequalities' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Graph linear inequalities in two variables
- Interpret feasible regions in context
- Interpret intersections as solutions to systems
- Solve linear inequalities in one variable
- Solve systems of linear equations algebraically
- Solve systems of linear equations graphically
- Solve systems of linear inequalities graphically
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Systems and Inequalities) through scaffolded problems that grow in difficulty as concepts are understood.