# How do solve the following linear system?:  -6x+5y=1 , 7x+2y=2 ?

Feb 21, 2018

By substitution.
$x = \frac{8}{47}$, $y = \frac{19}{47}$

#### Explanation:

$- 6 x + 5 y = 1$
$+ 7 x + 2 y = 2$

We can take out x of the first equation, for example ;

$x = \frac{5 y - 1}{6}$

and we substitute it into the second equation and make all denominators equal :

$7 \left(\frac{5 y - 1}{6}\right) + 2 y = 2$

$\frac{35 y - 7}{6} + \frac{12 y}{6} = \frac{12}{6}$

Multiply both sides by $6$.

$35 y - 7 + 12 y = 12$

$47 y = 19$

$y = \frac{19}{47}$

Then we take this value and put it into our equation for $x$.

$x = \frac{\left(\frac{95}{47}\right) - 1}{6}$

$x = \frac{\frac{48}{47}}{6} = \frac{\cancel{48}}{47} \cdot \frac{1}{\cancel{6}} = \frac{8}{47}$