# Nonlinear Systems of Equations

A system of equations is nonlinear when at least one of its equations is not in the first degree.

The solution of these systems is usually done by the substitution method. To execute this method, follow the following steps:

1. Work out the value of an unknown in one of the equations, preferably in an equation of the first grade.

y = 7 − x

2. Substitute the value of the unknown in the other equation.

x^{2} + (7 − x)^{2} = 25

3.Solve the resulting equation.

x^{2} + 49 − 14x + x^{2} = 25

2x^{2} − 14x + 24 = 0

x^{2} − 7x + 12 = 0

4. Each of the values obtained are substituted into the other equation, and corresponding values of another unknown are obtained.

x = 3 y = 7 − 3 y = 4

x = 4 y = 7 − 4 y = 3

#### Examples

#### Word Problem

The product of two numbers is 4, and the sum of their squares 17. What are these numbers?