Question

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

Answer 1

The graphical representation of $3y-5x=30$ is given as
dotted line in the figure above. This line divided the $xy-$ plane in two half planes
Select a point (not on the line), which lies in one of the half
planes, do determine whether the point satisfies the given inequality or not.We select the point as $(0,0)$
It is observed that,
$3\left(0\right)-5\left(0\right)<30or0>30$, which is true
Therefore, upper half plane is not the solution region of the
given inequality. Also, it is evident that any point on the
lines does not satisfy the given strict inequality.
Thus, the solution region of the given inequality is the
shaded half plane containing the point $(0,0)$ excluding
the line.The solution region is represented by the shaded region as as
above.