There are various proposals for solving systems with a severe sign problem:

This also allows us to approximately solve systems where n is so large that the direct method would take too much time.

Using computers to solve systems of linear equations is used every day.

Procedure functions can also be used to solve systems of equations.

Circuit analysis is the study of methods to solve linear systems for an unknown variable.

This eliminates the need to construct and solve large systems of equations.

They have also been developed for solving nonlinear systems of equations.

It was designed to solve systems of differential equations and modeling processes.

Note also how the procedure works by solving just linear systems, in which the matrix remains constant.

It came from mathematicians trying to solve systems of linear equations.