How to Graph Non Linear Equations

Introduction:

An equation which have two or more than two degree of variables is known as non linear equation. In non linear systems one equation is linear and another one is non linear, here substitution is the easiest method to solve the problem. In the system of non linear equation, the linear equation is to be solved for either x or y, then substitute the resulting expression into the nonlinear equation. A non linear equation can be represented geometrically by a line whose points make up the collection of solutions of the equation.

Example:

Solve the following non linear system of equation

y = 3x + 2

y = x² + 2x – 3

Solution:

Here the one equation is linear while the other equation is non linear

Plug first equation in equation two.

y = 3x + 2

3x + 2 = x² + 2x – 3

Subtract 3x and 2 on both sides

3x + 2 – 3x – 2 = x² + 2x - 3 - 2 – 3x

x² – x – 5 = 0

Here we have to use quadratic formula to solve this equation

x = (- b ± `sqrt(b2-4ac)`) / 2a