# How do you solve the following system: 5x - 7y = 12 , 2x + 5y= 2 ?

Dec 6, 2015

$5 x - 7 y = 12$ (Consider this equation as equation 1)
$2 x + 5 y = 2$ (Consider this equation as equation 2)

$x = \frac{7 y + 12}{5}$ (From equation 1)
Substitute this value of x in equation 2
$2 \frac{\left(7 y + 12\right)}{5} + 5 y = 2$
$14 y + 24 + 25 y = 10$
$39 y = - 14$
$y = - \frac{14}{39}$
Substitute this value of y in equation 1
$5 x - 7 \left(- \frac{14}{39}\right) = 12$
$195 x + 98 = 468$
$x = \frac{370}{195}$
$x = \frac{74}{39}$