Question

Solve the following inequations graphically in two-dimensional plane.
y ≤ – 2x

Answer 1

Consider the equation y = 2x.
This is the equation of a line passing through origin in third and fourth quadrant inclined.
more towards Y-axis.

Consider a point (2, 1).
Substitute in equation
y ≤ – 2x
⇒ 1 ≤  2(2)
⇒ 1 ≤ –  4
shows that point (2,  1) does not satisfy the inequation.
The solution is in the other plane away from that point.