# What is the difference between a system of linear equations and a system of nonlinear equations? Question
Equations What is the difference between a system of linear equations and a system of nonlinear equations? 2021-03-08
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.

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Q) The system of differential equations $$\displaystyle{x}′={t}{y}+{5}{\left({\sin{{t}}}\right)}{y}−{3}{e}^{{t}},{y}′={t}^{{2}}{x}−{7}{x}{y}−{1}$$ is a ﬁrst-order linear system of differential equations. When solving systems of equations we have at least two unknowns. A common example of a system of equations is a price problem. For example, Jacob has 60 coins consisting of quarters and dimes.
The coins combined value is \$9.45. Find out how many of each (quarters and dimes) Jacob has.
1.What do the unknowns in this system represent and what are the two equations that that need to be solved?
2.Finally, solve the system of equations.  3.(-1,7) $$\displaystyle{\left\lbrace\begin{array}{c} {4}{x}+{y}={3}\\{2}{x}-{3}={y}\end{array}\right.}\rbrace$$ 