Solve the following system of inequalities graphically:

x + y ≤ 6, x + y ≥ 4

Given. x + y ≤ 6,

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

Y = 6 and x = 6

The required points are (0,6 ) and (6,0)

Checking further for origin (0,0)

We get 0 ≤ 6, this is true.

Hence the origin would be included in the area of the line`s graph. So the required solution of the equation would be on the left side of the line graph which will be including origin.

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 required points are (0,4 ) and (4,0)

Checking for the origin (0, 0)

0 ≥ 4 which is false

So the origin would not be included in the required area. The solution area will be above the line graph or the area on the right of line graph.

Hence the shaded area in the graph is required graph area.