# How do you solve x = 4y + 8 and 2x - 8y = -3?

Nov 5, 2015

This system has no solutions.

#### Explanation:

This system has no solutions. Multiplying by $2$ the first equation, we have

$2 x = 8 y + 16$, which we can rewrite as $2 x - 8 y = 16$. So, the system becomes

$\left\{\begin{matrix}2 x - 8 y = + 16 \\ 2 x - 8 y = - 3\end{matrix}\right.$

And you can see this is impossible: if the same quantity (namely $2 x - 8 y$) is equal to both $16$ and $- 3$, then also $16 = - 3$, which is clearly false.