Is it possible to solve a linear inequality system using SVD?I have a large linear...

No; loosely speaking this problem is more related to linear programming, which is not equal to linear algebra. (Plugging in an SVD of $A$ will be too helpful as you probably have seen.)
The set $Ax\le 0$ is a convex polytope and the representation $Ax\le 0$ is called its H-representation because it is a description as intersection of half-spaces. Another representation is its V-representation which consists of a list of the vertices.