# How do solve the following linear system?:  x-3y=-1 , 6x-4y=-1 ?

Nov 24, 2015

$x = \frac{1}{14}$, $y = \frac{5}{14}$

#### Explanation:

Since both expressions equal $- 1$, the expressions must equal each other. So, we know that

$x - 3 y = 6 x - 4 y$, and thus $5 x = y$.

Substitute this relation for $y$ in the first equation, to obtain

$x - 3 \left(5 x\right) = - 1$, and so $- 14 x = - 1$, and finally $x = \frac{1}{14}$.

Since $y$ is five time $x$, then we have $y = \frac{5}{14}$.