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