How do you solve the following linear system: y - 2x = -6 , 7x - y = 3 ?

Mar 17, 2018

$\left(x , y\right) = \left(- \frac{9}{5} , - \frac{48}{5}\right)$

Explanation:

$y = 2 x - 6$ solve for y in terms of x
$7 x - \left(2 x - 6\right) = 3$ plug in above equation to y
$7 x - 2 x + 12 = 3$ distribute
$5 x = - 9$ isolate
$x = - \frac{9}{5}$ solve
$y - 2 \left(- \frac{9}{5}\right) = - 6$ plug back into original equation
$y + \frac{18}{5} = - 6$ multiply
$y = - \frac{48}{5}$ isolate
$\left(x , y\right) = \left(- \frac{9}{5} , - \frac{48}{5}\right)$