How do you solve by substitution x + 7y = 33 and 3x - 2y = 7?

Jun 7, 2015

$x + 7 y = 33$

x = color(red)(33 - 7y .......equation $\left(1\right)$
$3 x - 2 y = 7$........equation $\left(2\right)$

Substituting equation $\left(1\right)$ in $\left(2\right)$ to find $y$

$3 \textcolor{red}{\left(33 - 7 y\right)} - 2 y = 7$

$99 - 21 y - 2 y = 7$
$- 23 y = 7 - 99$
$- 23 y = - 92$
color(blue)(y= 4

Substituting $y$ in equation $\left(1\right)$to find $x$
$x = 33 - 7 y$

$x = 33 - 7.4 = 33 - 28$
color(blue)(x =5

The solution for the system of equations is:
color(blue)( x = 5 , y=4