Question

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

Answer 1

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 `8y` to each side in order to isolate the `x`. We now have `x = 2 + 8y`.

We can plug this into the first equation. `-(2 + 8y) + 3y =2`. By distributing we can get `-2 -8y + 3y =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 + 8y`. So we can say that `x = 2 + 8(-0.8)`. That solves out to be `x = -4.4`. We can plug this back into the original equations.

`-x+3y =2 => -(-4.4) + 3(-0.8) = 2`
Then, `4.4 + -2.4 = 2`, and `2 =2`.