Question

How do you solve the following system?: `13x -17y =21, -7x -4y = -7`

Answer 1

`(307/171,-238/171)`

Explanation:

Multiply the first equation by 7, and the other by 13.

`7*(13x-17y) =7*21`
`91x-119y=147`

`13*(-7x-4y)=13*-7`
`-91x-52y=91`

Then add these two equations.

`91x-119y=147`
`-91x-52y=91`

`91x-119y-91x-52y=147+91`
`-171y=238`
`y=-238/171`

Now write `-238/171` instead of `y` in one of the equations.

`-7x+4*238/171=-7`
`x=307/171`