# How do you solve the following linear system -x + 3y = 2 , x -8y =2 ?

Nov 14, 2015

Using substitution, $x = - 4.4$ and $y = - 0.8$.

#### Explanation:

You can use substitution.

Our first step is to isolate a variable to one side, so that we can plug it in for variable wherever. What I notice first is that we have a positive $x$ in the second equation. Therefore, I can add $8 y$ to each side in order to isolate the $x$. We now have $x = 2 + 8 y$.

We can plug this into the first equation. $- \left(2 + 8 y\right) + 3 y = 2$. By distributing we can get $- 2 - 8 y + 3 y = 2$. By solving out this equation, we end up with $y = 0.8$.

Now we can plug $y$ back into our equation that says $x = 2 + 8 y$. So we can say that $x = 2 + 8 \left(- 0.8\right)$. That solves out to be $x = - 4.4$. We can plug this back into the original equations.

$- x + 3 y = 2 \implies - \left(- 4.4\right) + 3 \left(- 0.8\right) = 2$
Then, $4.4 + - 2.4 = 2$, and $2 = 2$.