For the following exercise:

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-oo <= -1 x[0] + 1 x[1] + 3 x[2] <= 1

-oo <= -2 x[0] + -4 x[1] + 1 x[2] <= 3

-oo <= -2 x[0] + 2 x[1] + 4 x[2] <= 4

-4 <= -3 x[0] + 1 x[1] + 3 x[2] <= -4

4 <= 1 x[0] + 3 x[1] + 4 x[2] <= +oo

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the solution of the online tool is the following:

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-oo <= (2/3) x[0] <= (5/3)

-oo <= 0 x[0] <= 0

-oo <= (36/13) x[0] <= 15

-oo <= (8/5) x[0] <= (62/5)

-oo <= (48/19) x[0] <= (274/19)

-oo <= 0 x[0] <= 14

-oo <= 0 x[0] <= (42/5)

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Eliminated variable x[0] which is not both-bounded:

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-oo <= 0 <= 0

-oo <= 0 <= 14

-oo <= 0 <= (42/5)

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The final constraints are satisfiable.

A solution will be computed while returning from recursive calls.

Computed solution x[0] := (5/2)

Computed solution x[1] := (13/2)

Computed solution x[2] := -1

The given linear inequalities are solved!

I understand why x0 = 5/2 and x1 =13/2 and x2 = -1 are a working solution.

However, when I try to choose another value for x0 and calculate x1 and x2 from it, it is not accepted by the exercise system.

I tried using:

x0 = 7,75

x1 = -9,25

x2 = -18,5

which I got from the line: **-oo <= (8/5) x[0] <= (62/5)**

Is this also a solution which the exercise system just doesn't accept or is there something wrong with this solution?

Also another question:

Why is the step

Eliminated variable x[0] which is not both-bounded:

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-oo <= 0 <= 0

-oo <= 0 <= 14

-oo <= 0 <= (42/5)

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needed? Do we need to check if any of the formulas is wrong?

What happens if one of the formulas is like this: **-oo <= 0 <= -4 **

This is obviously wrong. Do we stop then and say that no solution can be found?