Solve the following system of inequalities graphically:

x + y ≥ 4, 2x – y < 0

Solving for x + y ≥ 4

Putting value of x = 0 and y = 0 in equation one by one, we get value of

y = 4 and x = 4

The points for the line are (0, 4) and (4, 0)

Checking for the origin (0, 0)

0 ≥ 4

This is not true,

So the origin would not lie in the solution area. The required region would be on the right of line`s graph.

2x – y < 0

Putting value of x = 0 and y = 0 in equation one by one, we get value of

y= 0 and x = 0

Putting x = 1 we get y = 2

So the points for the given inequality are (0, 0) and (1,2)

Now that the origin lies on the given equation we will check for (4,0) point to check which side of the line`s graph will be included in the solution.

⇒ 8 < 0 which is not true, hence the required region would be on the left side of the

line 2x-y < 0

The shaded region is the required solution of the inequalities.