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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