Excel formula to solve a mathematical issue

Hi guys,

I have a mathematical issue I would like to solve using Excel.
The column A shows 3 values (e.g. 1, 2 and 3 but countless combinations are possible). The column B shows 3 unknown quantities (x, y and z). I need to find the value of x, y and z in order to get contemporaneously positive values in C1, C2 and C3. Is there a way to create an excel formula which can help me with that?

Please check the attachment to get more info.

Thanks in advance for your help!