Question

Represent to solution set of each of the following inequations graphically in two dimensional plane:

4. x − 2y < 0 

Answer 1

Converting the inequation to equation, we obtain x \[-\] 2y =0
Putting y = 0 and x = 0 in this equation, we obtain x = 0 and y = 0 respectively. So, this line meets the x-axis at (0,0) and the y- axis at (0,0).
If x = 1, then y = 1/2.
So, we have another point (1,1/2).
We plot these points and join them by a thin line. This divides the xy plane into two parts.
We take a point (0, 2) and it does not satisfy the inequation.

Therefore, we shade the region which is opposite to the point (0, 2)
The shaded region is the solution to the inequation.