We observe that
= 0 satisfy the
inequality. Thus, we say that the half plane I is the
graph (Fig 6.7) of the inequality. Since the points on
the line also satisfy the inequality (1) above, the line
is also a part of the graph.
Thus, the graph of the given inequality is half
plane I including the line itself. Clearly half plane II
is not the part of the graph. Hence,
inequality (1) will consist of all the points of its graph
(half plane I including the line).
We shall now consider some examples to
explain the above procedure for solving a linear
inequality involving two variables.
> 6 graphically.
Graph of 3
= 6 is given as dotted line in the Fig 6.8.
This line divides the
-plane in two half
planes I and II. We select a point (not on the
line), say (0, 0), which lies in one of the half
planes (Fig 6.8) and determine if this point
satisfies the given inequality, we note that
3 (0) + 2 (0) > 6
0 > 6 ,
which is false.
Hence, half plane I is not the solution region of
the given inequality. Clearly, any point on the
line does not satisfy the given strict inequality.
In other words, the shaded half plane II
excluding the points on the line is the solution
region of the inequality.
0 graphically in
two dimensional plane.
Graph of 3
– 6 = 0 is given in the
We select a point, say (0, 0) and substituting it in
given inequality, we see that:
3 (0) – 6
or – 6
0 which is false.
Thus, the solution region is the shaded region on
the right hand side of the line