Graph the solution sets of the following inequations:
x - y≤3
Given x - y≤3
⇒ - y≤ 3 - x
Multiplying by minus on both the sides, we’ll get
y ≥ - 3 + x
y ≥ x - 3
Consider the equation y = x - 3.
Finding points on the coordinate axes:
If x = 0, the y value is - 3 i.e, y = - 3
⇒ the point on the Y axis is A(0, - 3)
If y = 0, 0 = x - 3
⇒x = 3
The point on the X axis is B(3,0)
Plotting the points on the graph: fig. 2a
Now consider the inequality y ≥ x - 3
Here we need the y value greater than or equal to x - 3
⇒ the required region is above point A.
Therefore the graph of the inequation x + y ≥ 4 is fig. 2b
Fig 2a
Fig 2b