Question

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

x + 2y − y ≤ 0 

Answer 1

\[\text{ We have }, \]
\[x + 2y - y \leq 0\] 

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.