What's the difference between linear, quadratic and simultaneous equations?

In a linear equation the highest degree of the variable is 1. For example

3x + 1 = 2 is linear (x is of degree 1).

The graph of the function will be a straight line.

A quadratic equation will have degree 2 (eg x^2) and its graph will be curved. Example 3x^2 - x + 7 = 0

Simultaneous equations are 2 or more equations with 2 or more variables. For example

2x + y = 3

x - y = 1

They may be both linear, quadratic or or a mixture of both.