01
Linear systems
Interpret several half-plane or interval conditions together.
System of Inequalities Solver
Purpose-built solver page
System of Inequalities Solver
Use this system of inequalities solver to reason about the values that satisfy several inequalities at once. It explains boundaries, test points, and the overlapping solution set without promising an interactive graph.
Type or upload a problemWorked explanationsNo sign-up required
Solve a problem nowsystem of inequalities solver
{ y > x
Linear systems
Boundary conditions
Overlapping solution sets
system of inequalities solver
Solve your system of inequalities problem
Enter your system of inequalities problem below. Add the variable, conditions, and method you want so the AI can return a more relevant worked response.
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system of inequalities solver
What this System of Inequalities solver is designed for
The page is organized around the problem types people actually search for, while staying within the text-and-image solver's current capabilities.
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Boundary conditions
Distinguish strict boundaries from included boundaries.
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Overlapping solution sets
Use intersection to keep only values satisfying every inequality.
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Feasibility questions
Translate limits or constraints into a system and interpret whether a common solution exists.
Step
How to use the System of Inequalities solver
A complete prompt usually produces a more useful explanation than an isolated expression.
- 1
Enter all inequalities
{ y ≥ 2x − 1Put each condition on its own line and state the variables.
- 2
Find each boundary
y = 2x − 1Replace the inequality sign with equality to identify the dividing line or point.
- 3
Test the required side
(0, 0) → 0 ≥ −1Use a test point to decide which side satisfies each condition.
- 4
Take the overlap
A ∩ BDescribe the region or set that satisfies every inequality simultaneously.
Tip: ask for a named method, a domain, or a verification step when your course requires one.
system of inequalities solver
Boundary conditions
Distinguish strict boundaries from included boundaries.
Boundary conditions
y > mx + b ⋯Distinguish strict boundaries from included boundaries.
Boundary conditions
y ≥ mx + b ━Distinguish strict boundaries from included boundaries.
Overlapping solution sets
A ∩ BUse intersection to keep only values satisfying every inequality.
Overlapping solution sets
Use intersection to keep only values satisfying every inequality.
x > −2(−2, ∞)x ≤ 4(−∞, 4]2x + 1 ≥ 3[1, ∞)Example
System of Inequalities problems to try
These examples reflect common search intent and can be inserted into the solver as a starting point.
Example 1
Solve:
y >= 2x - 1
y < -x + 5Two linear conditions whose solution is their overlap.
Example 2
Solve:
x + y <= 8
x >= 0
y >= 0A feasibility region with nonnegative-variable constraints.
Example 3
Solve:
x > -2
x <= 4
2x + 1 >= 3A one-variable system combined by interval intersection.
Formula guides
Understand the formulas used here
Review the related formulas, when to use them, and how they connect in a worked example.
Common mistakes to watch for
A worked answer is most useful when you know which details are easy to lose along the way.
Solving conditions separately only
The final answer must satisfy every inequality, so take their intersection.
Using the wrong boundary type
Strict inequalities exclude the boundary; ≤ and ≥ include it.
Assuming a graph is the proof
Check a representative point algebraically and state the conditions clearly.
System of Inequalities solver FAQ
