A pair of equations like this are called simultaneous equations - because you are trying to solve them both with the same values for \(x\) and \(y\).

That way it is possible to find the only pair of values that solve both equations at the same time. These are known as simultaneous equations. The unknowns of \(x\) and \(y\) have the same value ...

For more information on these methods, see the references at the end of this chapter. There are two fundamental methods of estimation for simultaneous equations: least squares and maximum likelihood.