Graphing Linear Inequality Systems
A system of linear inequalities describes many rules at once. Each rule limits x, y, or both. The answer is not one point. It is a region. This calculator helps you draw that region and inspect it.
Why Graphing Helps
A graph makes hidden limits visible. One boundary may cut the plane in half. Another boundary may remove more space. The shared area is the feasible region. Any point inside that area satisfies every rule. A point outside fails at least one rule.
This method is useful in algebra, business planning, diet problems, production limits, and scheduling. It is also helpful before linear programming. You can see whether a model is possible before adding an objective function.
What The Solver Checks
The calculator first reads each inequality. It changes every rule into standard form, ax + by compared with c. The boundary line is then ax + by = c. For less than or equal signs, the valid side is below the line after testing. For greater than or equal signs, the opposite side is used.
The tool finds boundary intersections. Then it tests each intersection against all inequalities. Passing intersections become feasible corner points. The visible graph is clipped to your chosen window. This keeps the drawing clear, even when the region is unbounded.
Understanding Results
A vertex list shows the corner points of the closed feasible region. Strict inequalities use open boundaries in theory. Their limiting lines are still useful for graphing. A sample point confirms that the displayed region is valid. The visible area is only measured inside the graph window.
A region that touches the window may continue forever. Increase the range to inspect more of it. If no region appears, check your signs first. Then widen the graph window. Some systems have no solution. Other systems are simply outside the selected view.
Use the calculator as a checking tool. Write the system carefully. Review the graph and vertices. Then compare the result with hand shading. This builds confidence and helps you catch sign mistakes.
Good graph choices matter. Use ranges that include expected intercepts. Keep numbers simple when learning. Save CSV or PDF files for records. Keep class notes and repeated checks easy later.