The procedure for drawing the graph of inequality is similar to that of a linear graph.

The additional point to note here will be the shading of regions in the graph of inequality.

**Boundaries within regions **

The required boundary of a particular region is described by the equality sign =

However if the inequality sign is:

1. \( \scriptsize < \: or \: > \): the points on the boundary region are to be excluded, and for this, broken lines are used to draw the graph.

2. \( \scriptsize \leq \: or \: \geq \) : the points on the boundary region are included, and for this, continuous (straight unbroken) lines are used.

### ExampleÂ 1

1. Draw the graph of 3x + 2y < 12

When x = 0, y = 6 When y = 0, x = 4

### Example 2

2. Draw the graph of 4x + 3y â‰¥ 24

When x = 0, y = 8

When y = 0, x = 6

Simultaneous linear inequalities in two variables

### Example 3Â

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

4x – y â‰¤ 8Â

3x +2y > 12

Let us consider the inequality 4x – y â‰¤ 8 first.

To get the boundary line, first make y the subject

i.e 4x – y = 8

-y = 8 – 4x

y = -8 + 4x

When x = 0, y = -8. This gives point (0, – 8)

When y = 0, x = 2. This gives points (2, 0)

Mark out these two points on your axis and then join them together with a solid line

We consider the second inequality 3x + 2y > 12.

To get the boundary line which must be a broken line.

When x = 0, y = 6. This gives point (0, 6)

When y = 0, x = 4. This gives points (4, 0).

The solution lies within the region bounded by area ABC.

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