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Imagine I got 2 conditions or informations to find a unknown number x and did many steps ( of course mathematically correct with no mistake) using both conditions to find a value of x. Is it possible, to replace x and see it not work for any reason? Example: We get two equations with unknowns we use the substition method and get x and then we get and y with all mathematically valid steps and then we see that these y and x does not valid both equations.Can this happen? and can we get a false value of x;y when the system has no solutions?

Selim Jean Ellieh
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    If you preserve the domain for each operation, the situation you describe cannot happen. Post a concrete example if you have one. – Vasili Apr 02 '19 at 19:03

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If all steps were mathematically valid, and if you are interpreting each mathematical step correctly, then you should always see the result working. If not, you are probably violating a mathematical assumption, or you are missing another piece of information, or you are misinterpreting the result.

To answer your specific example, we are given 2 equations. I will break it up into cases:

$1)$ There are less than 2 unknowns. In this case, you can always find a solution and it will always work

$2)$ There are 2 unknowns. In this case, you you can either (a) find infinitely many solutions (b) find finitely many solutions (c) find that there are no solutions. Your solutions will always work

$3)$ There are more than 2 unknowns. In this case, it is generally impossible to find solution. But you may be able to get a partial answer in terms of the other unknowns, or find that the problem can be reduced to 2 unknowns and hence solveable

NazimJ
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