# System of linear equations: Unique, infinite and no solutions

**Unique solution** there is only one set of variables that satisfy all equations. Intersection is a point.

**No solutions** no set of variables satisfy all equations, usually you get 1 = 0 when solving the system. No intersection of all equations in one point.

**Infinite amount of solutions** infinite amount of variables satisfy the equation, meaning at least one free variable. Intersection in a line or plane.

Example: Solve the system of linear equations:

(1.1)3 + y = 2 ⇒ y = −1

The answer is: (1,−1). It can also be represented graphically, as an intersection of two lines in a single point.

Example: Solve the system of linear equations:

Example: Solve the system of linear equations:

Which is not true, thus there are no solutions to this system of linear equations. It can be seen as three planes that do not intersect in the same point: