# How do you solve the system of equations 2x-y=71 and 3y=x using substitution?

Feb 17, 2017

$\left(\frac{142}{5} , \frac{71}{5}\right)$

#### Explanation:

$2 x - y = 71$ and $3 y = x$

you just substitute one equation into the other
since $x = 3 y$ you can just insert that into $2 x - y = 71$

$2 \left(3 y\right) - y = 71$
$6 y - 6 = 71$
$5 y = 71$
$y = \frac{71}{5}$

then we plug this y-value into either equation
$2 x - \frac{71}{5} = 71$
$2 x = \frac{284}{5}$
$x = \frac{284}{10} = \frac{142}{5}$

$\left(\frac{142}{5} , \frac{71}{5}\right)$