A system of nonlinear equations is two or more equations, at least one of which is not a linear equation. A system of equations where one or more equations involved is not a line. There are three possible outcomes that you may encounter when working with System of Equation that are not linear:

- a finite number of solutions
- no solution
- infinite solutions

Example for solving a nonlinear system by Elimination:

x^{2} + y^{2} = 4 (1)

2x^{2} - y^{2} = 8 (2)

Adding both equations 1 and 2 we get,

x^{2} = 4

x= -4,+4

for y substituting back into equation (1)

If x=2

2^{2} + y^{2} = 4

y^{2} = 4

y = 0

if x= -2

(-2)^{2} + y^{2} = 4

y^{2} = 0

y = 0

The solution set {(2,0) and (-2,0)}

Visualizing the types of graphs involved in a nonlinear system helps predict the possible numbers of ordered pairs of real numbers that may be in the solution set of the system.

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