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 the origin.

Therefore the graph of the inequation y≤is fig.8a

Fig 8a

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 the Y axis is A(0,2)

If y = 0, 0 = 2x + 2

⇒x = - 1

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

Plotting the points on the graph: fig. 8b.

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. 8c

Fig 8b

Fig 8c

Combining the graphs of 8a and 8c, we’ll get

The solution of the system of simultaneous inequations is the intersection region of the solutions of the two given inequations.