Example Graph the solution set of each of the following :
i) 2 x  y > 2 ii) x  2 y £ 4 iii) 2 x + y £ 0
Solution: i) Consider the line 2 x  y = 2 It meets x axis at (1,0) and y axis at (0, 2). The boundary is drawn passing through (0, 0). When we put x = 0 and y = 0 then the inequality, we get 0  0 > 2 i. e. 0 > 2. Thus the origin determined by the inequality is the halfplane which is the nonorigin side of the boundary line. Further it is a strict inequality (>) therefore, the solution set is the openhalf plane as shown in the figure.
ii) The bounding line is x2 y = 4 which meets x and y axis at points (4, 0) and (0, 2) respectively. The coordinates x = 0 and y = 0, satisfy the inequality x  2 y < 4 . Therefore, the graph of the solution set is the closed halfplane containing the origin as shown in the figure.
iii) The boundary line 2 x + y = 0 passes through (0, 0) and its slope is negative. If we put x = 1, y = 0 in 2 x + y £ 0 we get 2 £ 0. Hence (1,0) does not satisfy the inequality. Hence the graph of the solution set is the closed half plane which does not contain the point (1,0) as shown in the figure.
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Index
7.1 Definition
7.2 Simultaneous Equations
7.3 Inequations (Inequalities)
7.4 Absolute Values
Chapter 8
