# LINEAR INEQUALITIES

CONTENT

- Graphs of linear inequalities in two variables.
- Maximum and minimum values of simultaneous linear inequalities.
- Application of linear inequalities in real life.
- Introduction to linear programming

Graph of linear inequalities in two variables: We shall consider simultaneous inequalities.

**Examples**:

Show on a graph the region that contains the solution of the simultaneous inequalities

\(2x + 3y < 6,\) \(y -2x ≤ 2, y ≥ 0\)

Solution: In each case put \(y\) on one side of the inequality \(y < \frac{6 -2x}{3},\) \(y ≤ 2 + 2x\) and \(y ≥ 0\)

We shall draw the lines \(y =\frac{6 -2x}{3},\) \(y = 2 + 2x\) and \(y = 0\)

\(x\) | -2 | 0 | 2 | 3 |
---|---|---|---|---|

\(y_1 = \frac{6 -2x}{3}\) | 3.3 | 22 | 0.7 | 0 |

\(y_2 = 2 + 2x\) | -2 | 2 | 6 | 8 |

Points \(p_1(0, 0), p_2(1, 1)\) are in the solution set for the three inequalities.

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