Question

How do you solve the system of linear equations `x + 3y = 5` and `2x - y = 5`?

Answer 1

`20/7 = x`, `5/7 = y`

Explanation:

`x+3y = 5`

`2x - y = 5`

If both equations equal `5`, we can set them equal to eachother

`x + 3y = 2x - y`

`4y = x`

Now we can substitute `4y` for `x` in one of the equations (let's pick the first one)

`4y + 3y = 5`

`7y = 5`

`y = 5/7`

Now, if `4y = x`, then `4 xx 5/7 = x` or `x = 20/7`

Now to check our work. Let's substitute `5/7` and `20/7` for `y` and `x` in the second equation. If we have the correct answers, our equation should still equal `5`.

`2(20/7) - 5/7`

`40/7 - 5/7`

`35/7`, which simplifies to `5`! So we were correct.