In mathematics, any algebraic expression whose degree is one is known as linear expression. If any inequality holds a linear relation between the variables then such type of inequality is called as linear inequality. Like:
2x + y < 7, x - 2y + z > 4 etc, in these examples all the variables are presents in linear form, hence these are the linear inequalities.

A system of linear inequalities is a set of linear inequalities that we deal with all at once in the same plane. Usually a system of linear inequalities is just two or more than two inequalities together.
Generally a system of linear inequalities express as:
a11 x1 + a12 x2 +.........+ a1n xn $\leq or = or \geq $ b1
a21 x1 + a22 x2 +.........+ a2n xn $\leq or = or \geq $ b2
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
am1 x1 + am2 x2 +.........+ amn xn $\leq or = or \geq $ bm
Here x1 , x2,.....,xn are the unknown variables, a11, a12,.....,amn are the coefficients and b1, b2.....bm are the constants. This can be written as
AX $\leq or = or \geq $ B.