This tool helps you solve and graph systems of inequalities quickly and accurately.

## How to Use the System of Inequalities Calculator

This calculator helps you solve a system of two linear inequalities and find their intersection region if it exists.

Simply input two inequalities in the form of **inequality 1** and **inequality 2**. Use the format similar to “y >= 2x + 1”. Then click on the “Calculate” button.

### How the Calculator Works

Upon clicking the “Calculate” button, the calculator performs the following steps:

- Validate each inequality to ensure it follows the “y *= *x * *” format
- Parse and extract coefficients from each inequality
- Determine the intersection point by solving the system of inequalities

If both inequalities are valid, the calculator displays the intersection point of the inequalities.

### Limitations

The calculator currently only supports linear inequalities of the format “y *= *x * *”. Non-linear inequalities or other formats are not supported. Additionally, the calculator may have limitations for certain types of inequalities that are not easily parsed or solved.

## Use Cases for This Calculator

### Use Case 1: Finding Feasible Regions

Visualize and graphically analyze the overlapping areas between several inequalities quickly for both linear and nonlinear systems. Our system of inequalities calculator helps you determine the feasible regions where all inequalities are satisfied simultaneously. Easily identify the common shaded regions on the graph, allowing you to make informed decisions based on the constraints provided.

### Use Case 2: Optimizing Solutions

Utilize the calculator to find the optimal points of intersection in the feasible regions to maximize or minimize an objective function. By identifying the extreme points in the solution space, you can optimize your outcomes efficiently. Our tool provides a convenient way to visualize the points of interest on the graph for various optimization problems.

### Use Case 3: Solving Real-World Problems

Apply the system of inequalities calculator to solve real-world scenarios involving multiple constraints. Whether it’s resource allocation, production planning, or budgeting decisions, this tool helps you model and analyze complex systems conveniently. Make data-driven choices by visually mapping out the feasible solutions based on your input inequalities.

### Use Case 4: Fast Iterative Testing

Easily test different sets of inequalities and observe the changes in the feasible regions in real-time. Our calculator allows you to make quick adjustments to the constraints and instantly visualize the impact on the solution space. Speed up your iterative testing process and fine-tune your constraints efficiently with this versatile tool.

### Use Case 5: Educational Purposes

Teach and learn the concepts of system of inequalities effectively by using our intuitive calculator. Visualize the graphical representation of inequalities and their intersections to enhance your understanding of the subject. Whether you’re a student, educator, or enthusiast, this tool serves as a valuable learning aid for exploring the world of inequalities.

### Use Case 6: Sensitivity Analysis

Conduct sensitivity analysis by adjusting the coefficients of the inequalities and observing the changes in the feasible regions. Explore how variations in the constraints impact the feasible solutions and optimize your decision-making process. Our calculator empowers you to analyze the sensitivity of your system to different parameters efficiently.

### Use Case 7: Interactive Exploration

Interact with the graph by zooming in, panning, and exploring the details of the feasible regions effortlessly. Navigate through the plotted inequalities and visually inspect the intersection points with ease. Engage in an interactive exploration of your system of inequalities for a more immersive and insightful experience.

### Use Case 8: Exporting Results

Export the graph and solution data for further analysis or documentation purposes. Save the visual representation of the feasible regions as images or download the coordinates of critical points. Seamlessly transfer your results to presentations, reports, or other platforms for comprehensive analysis and communication.

### Use Case 9: Customizing Plot Options

Customize the plot options, such as colors, line styles, and labels, to enhance the visualization of your system of inequalities. Tailor the graph appearance to suit your preferences and improve the clarity of the plotted constraints. Personalize the plot settings to create visually appealing representations of your inequalities.

### Use Case 10: Multi-Constraint Analysis

Analyze systems with multiple constraints and observe the complex interactions between various inequalities. Explore the intricate relationships between the constraints and identify the overlapping regions efficiently. Gain valuable insights into multi-constraint scenarios and make data-driven decisions using our comprehensive calculator.