# Linear Inequalities in Two Variables

The inequalities of the form ${\text{ax}} + {\text{by}} > {\text{c}}$, ${\text{ax}} + {\text{by}} \leqslant {\text{c}}$, ${\text{ax}} + {\text{by}} \geqslant {\text{c}}$, where ${\text{a}} \ne 0$, ${\text{b}} \ne 0$, c are constants, are called the linear inequalities in two variables.

The points $\left( {{\text{x}},{\text{y}}} \right)$ which satisfy the linear inequality in two variables, ‘x’ and ‘y’ from its solution.

Graphing the Solution Region of Linear Inequality in Two Variables

Example:
Graph the solution set of the linear inequality ${\text{x}} - {\text{y}} \leqslant 1$ in xy–plane.

Solution:
We have

The corresponding equation of inequality A

For x–intercept:
Put ${\text{y}} = 0$ in equation (i)

For y–intercept:
Put ${\text{x}} = 0$ in equation (i)

Test:
Put origin $\left( {0,0} \right)$ in equation (A)

Which is true.
The solution set of inequality lies on the origin side.