# Solution to a System of Equations

## Solution to a System of Equations

The set of all values that can be substituted for the variables in each equation of a system and that satisfy all the equations of the system simultaneously.

### Example

Consider the system of equations y = 2x and y = 4x² − 1 :

The solutions to this system are the ordered pairs of coordinates ($$\frac{1 + \sqrt{5}}{4}$$,$$\frac{1 + \sqrt{5}}{2}$$) and ($$\frac{1 – \sqrt{5}}{4}$$,$$\frac{1 – \sqrt{5}}{2}$$).