6How many solutions exist? (1/2)

When you solve a linear system of equations, $3$ cases can occur:

1. When calculating the solution you find a wrong statement (e.g. $5$ = $3$).

2. You find out during the transformation that the equations are identical. The result is a statement that is true no matter which number you insert (e.g. $x = x$).

3. When calculating the solution you get a unique variable assignment for the equations of the system (e.g. $x = 5$ and $y=7$). This is the already known usualcase!

Panic. What to do in case 1. or 2.?

Don't worry! Even linear systems of equations cannot always be perfect. :-)

There are $3$ types of systems: Those with $\color{#009999}{none}$, $\color{#009999}{exactly \; one}$ or $\color{#009999}{infinitely \; many}$ solutions.