Solve the following system of inequalities graphically: x + y ≤ 9, y > x, x ≥ 0

Asked by Abhisek | 1 year ago |  91

##### Solution :-

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 lines 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 lines graph.

y > x,

Solving for y = x

We get x= 0, y = 0 so the origin lies on the lines 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 lines graph and hence would be on the left side of the line.

We have x ≥ 0

The area of the required lines graph would be on the right side of the lines graph.

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

Answered by Pragya Singh | 1 year ago

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