# How do you solve the linear equation x+3y=2 and -x+y=1 using the substitution method and are they dependent, independent, or inconsistent?

##### 1 Answer
Oct 22, 2017

$x = - \left(\frac{1}{4}\right) , y = \left(\frac{3}{4}\right)$
They are dependent and consistent.

#### Explanation:

$x + 3 y = 2$
#x = 2 - 3y color(white)(aaa) Eqn (2)

$- x + y = 1 \textcolor{w h i t e}{a a a}$ Eqn (1),

Substituting value of “x “ in Eqn (1),

$- \left(2 - 3 y\right) + y = 1$

$3 y + y = 3$
$4 y = 3 , \mathmr{and} y = \frac{3}{4}$

Substituting value of “y” in Eqn (1),

$- x + \left(\frac{3}{4}\right) = 1$
$- x = \frac{1}{4} , \mathmr{and} x = - \frac{1}{4}$

Verification :
Substituting value of “y” in Eqn (2),
$x = 2 - 3 y = 2 - 3 \left(\frac{3}{4}\right) = 2 - 2 \left(\frac{1}{4}\right) = - \left(\frac{1}{4}\right)$