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Solving Inequalities by Graphing

The solution of an inequality is represented on Graphs. Solutions of inequalities in one variables are represented as a part of a number line, while in the inequalities in two variables are represented as half planes in coordinate plane. Graphing method is generally used to solve system of inequalities.

Solving System of Inequalities by Graphing:
A system of inequalities consisting of two or more inequalities in two variables is solved using graphical method.

A linear inequality in two variables is represented by half planes in the coordinate plane.
To solve a system of linear inequalities, the boundary lines of all the inequality are graphed and the region common to them is shaded. This common region represents solution to the system.

Let us consider the system of inequalities,
x $\geq$ 1, y $\geq$ - 2 and 3x + 2y $\geq$ 8.
The boundary lines for the above system are x = 1, y = - 2 and 3x + 2y = 8. The boundary lines are graphed and the region common to three inequalities is shaded. The shaded region thus represents the solution to the system of inequalities.The graph for the solution of the system is shown below:

Solving Inequalities by Graphing

In the above graph, the vertices are A (1, -2), B (1, 2.5) and C (4, -2) and colored region represent the solution to the inequality system.

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