3Solve the following inequalities graphically in two-dimensional plane:

y – 5x < 30

Given: 3y – 5x < 30

Consider: 3y – 5x = 30

Now draw a dotted line 3y – 5x = 30 in the graph (∵3y – 5x = 30 is excluded in the given question)

Now Consider 3y – 5x < 30

Select a point (0,0)

⇒ 3 × (0) – 5 × (0) < 30

⇒ 0 < 30 (this is true)

∴ Solution region of the given inequality is below the line 3y – 5x < 30. (That is origin is included in the region)

The graph is as follows: