# How do you solve using the addition method and determine if the system is independant, dependant, inconsistant given 2y-x=3 and x=3y-5?

Jul 11, 2016

I found:
$x = 1$
$y = 2$
independent

#### Explanation:

We can add together, in columns, the two equations after a bit of rearranging to make them easier to add:
$\left\{\begin{matrix}- x + 2 y = 3 \\ x - 3 y = - 5\end{matrix}\right.$
color(red)(0-y=-2
So that $y = 2$
substituting back into, say, your first equation we get:
$- x + 4 = 3$
and: $x = 1$
One solution: system consistem and independent.