Set of coupled partial differential equations

Question

I've read that the Einstein equation is a set of 10 coupled partial differential equations. I know what a partial differential equation is, but I don't know what a set of coupled partial differential equations is. Please shed some light into this question.

Answer 1

A set of equations like $$\frac{\partial f}{\partial x} + \frac{\partial f}{\partial y}=a$$ $$\frac{\partial g}{\partial x} + \frac{\partial g}{\partial y}=b$$ where $g$ & $f$ are the dependent variable, $x$ & $y$ are the independent, $a$ & $b$ are constants
is a system of partial differential equations which are not coupled, which means that one could be solved without considering the second one. The solution of $f$ is independent of $g$.

A set of equations like $$\frac{\partial f}{\partial x} + \frac{\partial g}{\partial x} + \frac{\partial f}{\partial y}=a$$ $$\frac{\partial g}{\partial x} + \frac{\partial f}{\partial x} + \frac{\partial g}{\partial y}=b$$ is a system of coupled partial differential equations, which means that the solution of one dependent variable is depenting also on the other dependent variable and thus they sould be solved together in order to have a correct solution.