Question:
Solve the given inequality $3 x+5 y<15$ graphically in two-dimensional plane.
Solution:
The graphical representation of $3 x+5 y<15$ is given by blue dotted line in the figure below.
This lines divides $x-y$ plane into two parts.
Select a point (not on the line), which lies on one of the two parts, to determine whether the point satisfies the given inequality or not.
We select the point as $(0,0)$
It is observed that $0+0<15$ or $0<15$ which is true.
Therefore, the solution for the given inequality excluding the points on the line. This can be represented as follows,
