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# LINEAR INEQUALITIES

CONTENT

1. Graphs of linear inequalities in two variables.
2. Maximum and minimum values of simultaneous linear inequalities.
3. Application of linear inequalities in real life.
4. 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.

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS2 General Mathematics, SS2 General Mathematics Evaluation Questions, SS2 General Mathematics Evaluation Questions Second Term, SS2 General Mathematics Objective Questions, SS2 General Mathematics Objective Questions Second Term, SS2 General Mathematics Second Term
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