System of Linear Inequalities Calculator
Verified Calculation Engine
The online System of Linear Inequalities Calculator helps you calculate instantly and solve problems related to Linear Inequalities. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Solves system of linear inequalities and finds the solution region (intersection of all inequalities).
For system of inequalities:
a₁x + b₁ < c₁
a₂x + b₂ < c₂
...
Solution is intersection of all individual solutions
Solution of system is the intersection (AND) of all individual solutions
Inputs
Results
Worked Examples
Example 1: Two Inequalities
Solve system: 2x + 1 < 5 and x - 3 > -1
- inequalities: [ { "a": 2, "b": 1, "c": 5, "type": "<" }, { "a": 1, "b": -3, "c": -1, "type": ">" } ]
- solution: 2 < x < 2 (no solution)
- intervalNotation: No solution
- isFeasible: false
Example 2: Board Level
Solve system: x + 2 ≤ 5 and 2x - 1 ≥ 3
- inequalities: [ { "a": 1, "b": 2, "c": 5, "type": "≤" }, { "a": 2, "b": -1, "c": 3, "type": "≥" } ]
- solution: 2 ≤ x ≤ 3
- intervalNotation: [2, 3]
- isFeasible: true
About this calculator
Overview
System of Linear Inequalities Calculator evaluates System of Linear Inequalities for the math / linear-inequalities library. Primary input cue: Inequalities [required]: Array of inequalities in form [{a, b, c, type}, ...] for ax + b < c. Method anchor: For system of inequalities: a₁x + b₁ < c₁ a₂x + b₂ < c₂ ... Solution is intersection of all individual solutions. Solution of system is the intersection (AND) o.
When to use
Reach for System of Linear Inequalities Calculator to compare scenarios by changing one input at a time for system of linear inequalities.
Inputs explained
- Inequalities [required]: Array of inequalities in form [{a, b, c, type}, ...] for ax + b < c
Formula / method
For system of inequalities: a₁x + b₁ < c₁ a₂x + b₂ < c₂ ... Solution is intersection of all individual solutions. Solution of system is the intersection (AND) of all individual solutions (calculator id: system-of-linear-inequalities-calculator).
Worked example
Worked values: inequalities = [{'a': 2, 'b': 1, 'c': 5, 'type': '<'}, {'a': 1, 'b': -3, 'c': -1, 'type': '>'}] → solution = 2 < x < 2 (no solution), intervalNotation = No solution, isFeasible = False
Interpreting results
Cross-check with a simple numeric example before relying on extreme inputs for system of linear inequalities.
Assumptions
- Empty required inputs are not silently replaced with zeros for system of linear inequalities. [system-of-linear-inequalities-calculator]
- System of Linear Inequalities is computed only from the fields you enter on this calculator.
- Real-number arithmetic is used unless system of linear inequalities explicitly needs integers.
Limitations
- If multiple conventions exist for system of linear inequalities, this calculator uses the convention implemented in its engine path.
- This page does not provide a full textbook proof for every identity related to system of linear inequalities.
- Complex/branch cuts and undefined points are not always interactively annotated for system of linear inequalities.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
For system of inequalities: a₁x + b₁ < c₁ a₂x + b₂ < c₂ ... Solution is intersection of all individual solutions. Solution of system is the intersection (AND) of all individual solutions (calculator id: system-of-linear-inequalities-calculator).
Example Calculation
Worked values: inequalities = [{'a': 2, 'b': 1, 'c': 5, 'type': '<'}, {'a': 1, 'b': -3, 'c': -1, 'type': '>'}] → solution = 2 < x < 2 (no solution), intervalNotation = No solution, isFeasible = False
Frequently Asked Questions
What is System of Linear Inequalities Calculator?
- System of Linear Inequalities Calculator evaluates System of Linear Inequalities for the math / linear-inequalities library. Primary input cue: Inequalities [required]: Array of inequalities in form [{a, b, c, type}, ...] for ax + b < c. Method anchor: For system of inequalities: a₁x + b₁ < c₁ a₂x + b₂ < c₂ ... Solution is intersection of all individual solutions. Solution of system is the intersection (AND) o.
How does System of Linear Inequalities Calculator work?
- For system of inequalities: a₁x + b₁ < c₁ a₂x + b₂ < c₂ ... Solution is intersection of all individual solutions. Solution of system is the intersection (AND) of all individual solutions (calculator id: system-of-linear-inequalities-calculator).
Why use this Math Numbers calculator?
- Reach for System of Linear Inequalities Calculator to compare scenarios by changing one input at a time for system of linear inequalities.