Q. 93.8( 13 Votes )

Solve the following system of inequalities graphically:

5x + 4y ≤ 20, x ≥ 1, y ≥ 2

Answer :

Given 5x + 4y 20,


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


y = 5 and x= 4


The required points are (0, 5) and (4, 0)


Checking If the origin lies in the solution area (0, 0)


0 ≤ 20


Which is true, hence the origin would lie in the solution area. The required area of the line`s graph is on the left side of the graph.


x ≥ 1,


for all the values of y , x would be 1,


The required points would be (1, 0) , (1, 2) and so on.


Checking for origin (0, 0)


0 ≥ 1, which is not true


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


y ≥ 2


Similarly for all the values of x, y would be 2 .


The required points would be ( 0,2) , (1,2) and so on.


Checking for origin (0, 0)


0 2, this is no true


Hence the required area would be on the right side of the line`s graph.


The shaded area on the graph shows the required solution of the given inequalities.



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