Consider the inequation x - 2y ≥ 0:

⇒x ≥ 2y

⇒y≤

consider the equation y = . This equation’s graph is a straight line passing through origin.

Now consider the inequality y≤

Here we need the y value less than or equal to

⇒ the required region is below origin.

Therefore the graph of the inequation y≤ is fig.10a

Fig 10a

Consider the inequation 2x - y≤ - 2 :

⇒y ≥ 2x + 2

Consider the equation y = 2x + 2

Finding points on the coordinate axes:

If x = 0, the y value is 2 i.e, y = 2

⇒ the point on Y axis is A(0,2)

If y = 0, 0 = 2x + 2

⇒x = - 1

The point on X axis is B( - 1,0)

Now consider the inequality y ≥ 2x + 2

Here we need the y value greater than or equal to 2x + 2

⇒ the required region is above point A.

Therefore the graph of the inequation y ≥ 2x + 2 is fig. 10b

Fig 10b

y ≥ 0 is the region above X - axis

x ≥ 0 is the region right side of Y - axis

Combining the above results, we’ll get

As they is no common area of intersection , there is no solution for the given set of simultaneous inequations.