Question

How do you solve the system of equations `5x - 3y = 1` and `9x - 4y = 6`?

Answer 1

`x = 16/7`
`y = 73/21`

Explanation:

Firstly, you have to multiply each equation so there is the same number of a letter in each equation. In this case it is easier to make both `y`s equal `12`.
`5x - 3y = 1` should be multiplied by 4
#20x - 12y = 4

`9x - 4y = 6` should be multiplied by 3
`27x -12y = 18`

You can then take one equation away from the other. I will take the first away from the second:
`27x - 12y = 18`
`20x - 12y = 4` `-`
`(27x - 20x) + (-12y - -12y) = 18 - 4`
`7x = 16`
`x = 16/7`

You can then put this value of `x` into one of the original equations to get a value for `y`:
`(5 xx 16/7) - 3y = 1`
`3y = 80/7 - 1`
`3y = 73/7`
`y = 73/21`