# How do you solve the system of equations 13x - 5y = 20 and 13x - 5y = 10?

Dec 7, 2016

The system has no solution because its equations are incompatible.

#### Explanation:

Solve a system like this:

$13 x - 5 y = 20$
$13 x - 5 y = 10$

means we have to find values $x$ and $y$ that makes true both equations at same time.

In that system we have here, if we try to solve it, for example, using reduction method, we obtain something like that:

$\textcolor{w h i t e}{\text{.....}} 13 x - 5 y = 20$
$- \left(13 x - 5 y = 10\right)$
$\text{—————————}$
$\textcolor{w h i t e}{\text{.................}} 0 = 10$

i.e. a false identity. This means that no exists any value for $x$ and $y$ that match both equations at same time, i.e. system is incompatible.