# How do you solve the system using the substitution method for x-2y=3 and x+y=1?

Jul 30, 2015

The solution for the system of equations is
color(blue)( x=5/3, y=-2/3

#### Explanation:

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

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

Substituting equation $\left(1\right)$ in equation $\left(2\right)$
$x + y = 1$
$\textcolor{b l u e}{3 + 2 y} + y = 1$
$3 + 3 y = 1$

$3 y = 2$
color(blue)(y=-2/3

Substituting the value of $y$ in equation $\left(1\right)$ to find $x$
$x = 3 + 2 y$
$x = 3 + 2 \left(- \frac{2}{3}\right)$

$x = 3 - \frac{4}{3}$
color(blue)(x= 5/3