# How do you solve the system of equations -x + 4y = 0 and 2x + 5y = 0?

Aug 18, 2017

See below.

#### Explanation:

First glance tells us that we should consider $\left(0 , 0\right)$ as a solution, since both equations equal zero. Let's prove that this is the solution.

$4 y = x$

$2 x + 5 y = 0$

Plugging in the value for $x$,

$2 \left(4 y\right) + 5 y = 0$

$13 y = 0$ so $y = 0$.

From $4 y = x$, $4 \left(0\right) = x$ so $x = 0$.

Thus, our solution is $\left(0 , 0\right)$.