Solve the following inequalities graphically in two-dimensional plane 3y-5x< 30.

3y-5x = 30. ...(i)

Putting x' - 0, y - 10, therefore the point on the y-axis is (0,10).

The point on the j-axis is (-6,0). AB is the graph of (i). Putting x = 0, y = 0 in the given inequality, we have 3(0) - 5(0) < 30 or 0 - 0 < 30 or 0 < 30, which is true.

Hence, origin lies in the half-plane region I.

Clearly, no point on the line satisfies the given inequality.

Hence, the shaded region I excluding the points on the line is the solution region of the inequality.