# How do you know when a system of equations is inconsistent?

##### 1 Answer

When you try to solve the system, you get an impossibility.

You get something like

If you're working in the real numbers with nonlinear systems, you might instead get an imaginary solution.

(For example:

A system is inconsistent if, being a solution to one equation is **inconsistent with** being a solution of another equation in the system.

Being "inconsistent with" mean they can't both happen.

For example: being negative is **inconsistent with** being positive.

Being less than 4 is **inconsistent** with being greater than 9.

Being a solution to

(

The system:

is inconsistent.