Question

How do solve the following linear system?: `y = 8 x - 3 , x-3y=-1`?

Answer 1

`x=10/23 and y=11/23`

Explanation:

Substitute the first equation into the second - that is, in the second equation, wherever you see a `y` you replace it with `8x-3`.
Then the second equation becomes :
`x-3(8x-3)=-1`.

This is now 1 equation in 1 unknown and we may solve for `x` to obtain
`x-24x+9=-1`
`therefore x=-10/-23=10/23`.

Now substitute this value back into equation 1 to find `y` :

`therefore y=8(10/23)-3`
`=11/23`