# Question #b5882

Apr 10, 2017

$x = - \frac{22}{13}$ and $y = - \frac{29}{13}$

#### Explanation:

Ill do the first one as an example,

$x - 3 y = 5$ and $3 x + 7 y = 1$

The goal is to eliminate one of the variables so it is possible to solve for the other,

$x - 3 y = 5$ equation 1
$3 x + 7 y = 1$ equation 2

Multiply the first equation by $3$, and subtract the first equation from the second equation.

$3 x - 6 y = 30$
$3 x + 7 y = 1$

Subtracting the equations gives you,

$- 13 y = 29$
$y = - \frac{29}{13}$

Now knowing $y = - \frac{29}{13}$, you can solve for $x$. Do so by subsituting the value for $y$ into equation 1.

$x - 3 \left(- \frac{29}{13}\right) = 5$
$x + \frac{87}{13} = 5$
$x = 5 - \frac{87}{13}$
$x = - \frac{22}{13}$

Therefore,

$x = - \frac{22}{13}$ and $y = - \frac{29}{13}$