System of Linear Inequalities
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A system of linear inequalities refers to a set of two or more linear inequalities that are considered together. Each inequality represents a region of the coordinate plane, and the solution to the system is the set of points that satisfy all of the inequalities simultaneously.
For example, a system of linear inequalities might look like this:
y < 2x + 3
y > -x + 1
Each inequality describes a half-plane, and the solution to the system is the region where all the half-planes overlap.
To solve a system of linear inequalities, you typically graph each inequality on the same coordinate plane and find the region where the shaded areas (representing the solutions of each inequality) intersect. Points within the overlapping shaded region are solutions to the system.
In summary, a system of linear inequalities involves finding the set of points that satisfy all of the inequalities in the system at the same time.