Answer to Question #191559 in Linear Algebra for EUGINE HAWEZA

Question

Examine linear inequalities and how to formulate their graphical solutions

Answer 1

In graphical solutions of linear inequalities, solution can be divided into two subsets. 

for example, $2x+y\le 4$

One subset includes all values (x, y) that satisfy the equation 2x+y=4

and the other subset includes all the values (x, y) that satisfy 2x+y<4

First we plot 2x+y=4 on the graph and after that we see the region

By putting (0,0) in the inequality, and see of the conditions true or false-

if condition true- Solution region lies towards the origin.

condition false- solution region lies away from the origin.