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* = 2*x* and *y* = 4*x*² − 1 :

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