# How do you solve the system 2y+6=x and y-3x=-13 using substitution?

May 27, 2015

$2 y + 6 = x$ ...............equation $\left(1\right)$

$y - 3 x = - 13$
$y = - 13 + 3 x$........equation $\left(2\right)$

substituting equation $\left(2\right)$ in equation $\left(1\right)$
$2 y + 6 = x$
$2 \left(- 13 + 3 x\right) + 6 = x$
$- 26 + 6 x + 6 = x$
$6 x - x = 20$
$x = \frac{20}{5} = 4$

substituting this value of $x$ in equation 2
$y = - 13 + 3 x$
$y = - 13 + 3. \left(4\right)$
$y = - 13 + 12 = - 1$

the solutions for the system of equations are
 color(purple)(x=4 and y =-1