Is this way of solving equations correct mathematically?

We changed the system of equations that we were solving using fsolve to get better results by changing a parametre to a variable and adding an equation for the same. However, I am not confident on the way we are doing it. Hence, I am presenting a short example (since writing the exact equations might be confusing). It would be great to get suggestions if this way writing the equations is correct:

Original system: assume a and b are parameters,

3x-z = a;

2x+5y = b;

y = z;

The change in the system

3x-z = a;

2x+5y = b;

y = z;

2x+5z = b

[John D'Errico]

So what are the equations you are using in the second case? What you have written is identical to the first, having replaced z with y in one equation.

Are you thinking that since you have reduced the problem to one of 2 equations in 2 unknowns it is better? (Yes, by reducing the search space, of course this must be an improvement.)

But if you have 4 equations in the second case, that is a bad idea.

Regardless, the system you have posed is trivial, and should never be solved using fsolve anyway, since it is LINEAR! As well, fsolve cannot have unknown parameters. So a and b must be KNOWN parameters.