Q. 83.7( 17 Votes )

# Solve the following system of inequalities graphically:

x + y ≤ 9, y > x, x ≥ 0

Answer :

Given x + y ≤ 9,

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

y = 9 and x = 9

The required points are (0,9) and (9,0)

Checking if the origin is included in the line`s graph (0,0)

0 9

Which is true , so the required area would be including the origin and hence will lie on the left side of the line`s graph.

y > x,

Solving for y = x

we get x= 0, y = 0 so the origin lies on the line`s graph.

The other points would be (0, 0) and (2, 2)

Checking for (9, 0) in y > x,

we get 0 > 9 which is false, since the area would not include the area below the line`s graph and hence would be on the left side of the line.

x 0

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

∴ the shaded are is the required solution of the given inequalities.

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