Question

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

Answer 1

Consider the equation 2x – y ≤ – 2
∴ corresponding equation is 2x – y = – 2
∴ `(2"x")/-2-"y"/-2=(-2)/-2`
∴ `"x"/-1+"y"/2=1`
∴ intersection of line with X-axis is A (− 1, 0)
intersection of line with Y-axis is B (0, 2)
Origin test:
Substituting x = 0, y = 0 in the given inequation, we get
2(0) – 0 ≤ – 2
0 ≤ – 2
This shows that the origin is not satisfying the inequation.
∴ Points on the non-origin side of the line satisfy the inequation
∴ all the points on the line and above it satisfy the given inequation. The shaded portion represents the solution set.