System of Inequalities Solver

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Visualize the solution region for a system of linear inequalities.

Inequality Parameters

Inequality 1: yax + b

a (slope)

b (y-int)

Inequality 2: ycx + d

c (slope)

d (y-int)

Feasible Region

Point: (2.67, 2.67)

Intersection Point

The overlapping shaded region is the solution to the system.

Inequality 1

Inequality 2

Overlap = Solution

About this calculator

What is a System of Inequalities?

A system of linear inequalities is a set of two or more linear inequalities with the same variables. The solution to the system is the set of all points (x, y) that satisfy all inequalities simultaneously. Graphically, this is represented by the area where the shaded regions of each individual inequality overlap.

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Pro Tips

Use a solid line for ≤ or ≥ and a dashed line for < or >.
A test point (like 0,0) can help determine which side of the line to shade.
The overlapping region is often called the 'feasible region' in linear programming.

Fun Facts

"Systems of inequalities are the core of Linear Programming, used to minimize costs and maximize profits in business."
"The boundary lines represent the limits of resources (like time or money)."
"If the shaded regions do not overlap, the system has no solution."

Formula: Region: y > ax + b ∩ y < cx + d