How do you solve by substitution 3x + 2y = 2 and -2x + y = 8?

Jun 9, 2015

The solution for the system of equations is
 color(red)(x =-2 , y =4

Explanation:

$3 x + 2 y = 2$..........equation $\left(1\right)$

$- 2 x + y = 8$
 y =color(red)( 8 +2x............equation $\left(2\right)$

Substituting equation $\left(2\right)$ in equation $\left(1\right)$

$3 x + 2 y = 2$
$3 x + 2 \textcolor{red}{\left(8 + 2 x\right)} = 2$
$3 x + 16 + 4 x = 2$
$7 x = - 14$
 color(red)(x=-2

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

$y = 8 + 2 x$
$y = 8 + 2. \left(- 2\right)$
$y = 8 - 4$
 color(red)(y = 4