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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