How to solve a system of inequalities without graphing?
Here is one approach to solving it without graphing.
I think that you are asking about systems of inequalities in two variables, like
The system is equivalent to
We can write the solutions in "set-builder notation" as:
Combining these we write:
I think that for many people that way of writing the solution set is not as helpful as sketching the region of solutions in the coordinate plane.