Graph systems of linear and nonlinear inequalities with shaded feasible regions. Identify vertices and bounded regions.
This grapher shows where several inequalities are simultaneously true in the x-y plane. Enter linear or nonlinear conditions to display their boundary curves, shaded solution sets, and common feasible region. For polygonal systems, it can identify corner vertices and whether the overlap is bounded. The frequent mistake is reading the separate shaded sets as alternatives. A system uses their intersection: a point belongs only when it satisfies every entered inequality.
A concrete input and expected output from the current implementation.
Input
x >= 0 y >= 0 x + y <= 4
Expected output
A bounded triangular feasible region, including its edges, with vertices (0, 0), (4, 0), and (0, 4).
The first two inequalities restrict solutions to the first quadrant. The line x + y = 4 meets the axes at (4, 0) and (0, 4), and the <= condition keeps the side containing (0, 0).
Each inequality divides the plane using its equality boundary, such as x + y = 4 for x + y <= 4. The satisfying side of that boundary is shaded. When several inequalities are entered, the feasible region is their overlap, since every condition must hold at once. Strict operators exclude their boundaries, while >= and <= include them.
For linear constraints, corner candidates occur where boundary lines intersect. A valid vertex must also satisfy every inequality in the system. A region is bounded when it cannot continue indefinitely in any direction. Nonlinear boundaries can instead enclose smooth regions, such as disks, for which a finite list of polygon-style vertices may not describe the shape.
Check whether the inequality is strict. For x < 3, points with x = 3 are excluded because equality is not permitted. For x <= 3, those points are included. If several constraints meet at that boundary, the point must satisfy all of them, not merely the inequality whose line passes through it.
No. The grapher can expose the feasible polygon and its vertices, but the constraints alone do not define what should be maximized or minimized. A specified linear objective can be evaluated at valid vertices, with separate attention to ties, infeasibility, and unbounded objectives. The feasible-region graph by itself is not a complete optimization result.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Calculate percentages, percentage change, and what percent one number is of another with step-by-step breakdowns.
Calculate tips and split bills between multiple people with customizable tip percentages and rounding options.
Calculate monthly payments, total interest, and generate amortization schedules for loans and mortgages.
Calculate Body Mass Index from height and weight with category classification and healthy range guidance.
Calculate sale prices, savings amounts, and final costs after single or stacked percentage discounts.
Compute mean, median, mode, standard deviation, variance, and other descriptive statistics from a data set.