Question

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

1. x + 2y − y ≤ 0

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ x+2y-y\le 0 \end{gathered}$$

Converting the given inequation to equation, we obtain x + 2y $-$ y = 0, i.e x + y = 0
Putting y = 0 and x = 0 in this equation, we obtain x = 0 and y = 0.
So, this line intersects the x-axis and the y-axis at (0,0).
We draw the line of the equation x + y = 0
Now we take a point (1, 1) ( any point which does not lie on the line x + y = 0 )
(1, 1) does not satisfy the inequality. So, the region not containing (1, 1)
is represented by the following figure.

Hence, the shaded region represents the in equation.