System of linear equations is a collection of equations in which each equation in the system represents a straight ilne, that is the equations of degree 1( linear).

On the other hand, a nonlinear system of equations is a collection of equations that may contain some equations of a line, but not all of them.

For example,

\(\displaystyle{\left\lbrace\begin{array}{c} {x}+{y}={5}\\{3}{x}+{4}{y}={2}\end{array}\right.}\rightarrow\) system of linear equations.

\(\displaystyle{\left\lbrace\begin{array}{c} {x}+{y}={1}\\{y}+{x}^{{2}}-{5}\end{array}\right.}\rightarrow\) system of non - linear equations.

On the other hand, a nonlinear system of equations is a collection of equations that may contain some equations of a line, but not all of them.

For example,

\(\displaystyle{\left\lbrace\begin{array}{c} {x}+{y}={5}\\{3}{x}+{4}{y}={2}\end{array}\right.}\rightarrow\) system of linear equations.

\(\displaystyle{\left\lbrace\begin{array}{c} {x}+{y}={1}\\{y}+{x}^{{2}}-{5}\end{array}\right.}\rightarrow\) system of non - linear equations.