Steps for find solution region for a linear inequality in 2 variables
1 . Replace the inequality sign with equal sign & plot the graph . In this case plot graph for x + 2y = 9 . Green line represent x + 2y = 9
2 . Take any point on the graph . Here we took ( 10 , 10 ) & check if satisfies the linear inequality . In this case x + 2y > 9 . If yes , then the region where this assumed point lies is the solution region .
3 . In case of Slack inequality ( ≥ or ≤ ) use solid line , since the points on the line is included in the solution set .
4 . In case of Strict inequality (> or <) use dotted line , since points on the line is not included in solution set .
In case of multiple linear inequalities , the region common to all the inequalities is the solution region .
Numerical : Solve the following system of inequalities graphically 5x + 4y ≤ 40 & x > 2 & y ≥ 3