Systems of linear inequalities

In summary, a system of linear inequalities is a set of two or more linear inequalities that are graphed on the same coordinate plane. To graph a system of linear inequalities, each individual inequality is graphed and the region that satisfies all of the inequalities is shaded in. The main difference between a system of linear inequalities and a system of linear equations is the use of inequality signs instead of equal signs. The solution to a system of linear inequalities is the overlapping region of all the inequalities, which can be found through graphing or solving algebraically. And finally, a system of linear inequalities can have more than two variables, with each variable having its own coordinate plane and the solution being the overlapping region.
  • #1
sid_galt
502
1
Hi,
Is there a polynomial time algorithm (polynomial time in terms of the number of input constraints and variables) to solve a system of linear inequalities or or indicate whether a solution for a system of linear inequalities exists or not?
Thanks
 
Last edited:
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  • #2
Polynomial time Simplex?
 
  • #3
Simplex is exponential in the worst-case. Although there's Karmarkar's algorithm, it is for optimization of an objective function. Although it can be used for solving systems of linear inequalities, it takes n^3.5*L^2 time. I was wondering if there was a faster algorithm for giving a solution to the systems of linear inequalities.
 

Related to Systems of linear inequalities

1. What is a system of linear inequalities?

A system of linear inequalities is a set of two or more linear inequalities that are graphed on the same coordinate plane. The solution to the system is the region where all of the inequalities overlap.

2. How do you graph a system of linear inequalities?

To graph a system of linear inequalities, start by graphing each individual inequality on the same coordinate plane. Then, shade in the region that satisfies all of the inequalities.

3. What is the difference between a system of linear inequalities and a system of linear equations?

A system of linear equations has equations with an equal sign, while a system of linear inequalities has equations with an inequality sign (such as < or >).

4. How do you determine the solution to a system of linear inequalities?

The solution to a system of linear inequalities is the region where all of the inequalities overlap. This can be found by graphing the inequalities and identifying the overlapping region, or by solving algebraically.

5. Can a system of linear inequalities have more than two variables?

Yes, a system of linear inequalities can have more than two variables. These systems can be graphed on multiple coordinate planes, one for each variable, and the solution will still be the overlapping region.

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