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# 06 systems of linear inequalities

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### 06 systems of linear inequalities

1. 1. Systems of Linear Inequalities<br />
2. 2. Graphing a Linear Inequality<br />Solve the inequality for y, then <br />graph y = mx + b.<br />y >mx +b is satisfied above the line.<br />y = mx +b is satisfied on the line itself.<br />y < mx + b is satisfied below the line.<br />
3. 3. Example:<br />Graph the following:<br />y > x + 1<br />2y < x – 2<br />3x – 2y ≤ 6<br />
4. 4. Graphing a Linear Inequality<br />If the inequality involves x and not y, then graph the vertical line x =k.<br />x >k is satisfied to the right of the line.<br />x = k is satisfied on the line itself.<br />x < k is satisfied to the left of the line.<br />
5. 5. Graphing a Linear Inequality<br />If the inequality involves yand not x, then graph the horizontal line y =k.<br />y >k is satisfied above the line.<br />y= k is satisfied on the line itself.<br />y< k is satisfied below the line.<br />
6. 6. Example:<br />Graph the following:<br />x > 4<br />y ≤ 5<br />
7. 7. Solving Systems of Linear Inequalities<br />
8. 8. Graphical Method<br />To solve systems of two linear inequalities graphically, graph each of the linear inequalities on the same coordinate plane.<br />The region that is common to the inequalities is the solution set of the system.<br />
9. 9. Example:<br />Draw the graph of each of the following systems of inequalities and find the solution set. If the solution is a polygonal region, give the coordinates of the vertices of the boundary.<br />1. 3.<br />2. 4. <br />
10. 10. Example:<br />Draw the graph of each of the following systems of inequalities and find the solution set. If the solution is a polygonal region, give the coordinates of the vertices of the boundary.<br />5. 6.<br />
11. 11. Exercises:<br />Draw the graph of each of the following systems of inequalities and find the solution set. If the solution is a polygonal region, give the coordinates of the vertices of the boundary.<br />1. 3.<br />2. 4. <br />
12. 12. Exercises:<br />Draw the graph of each of the following systems of inequalities and find the solution set. If the solution is a polygonal region, give the coordinates of the vertices of the boundary.<br />5. 6. 7. <br />
13. 13. Exercises:<br />Draw the graph of each of the following systems of inequalities and find the solution set. If the solution is a polygonal region, give the coordinates of the vertices of the boundary.<br />8. 9. 10. <br />