Question

How do you solve `5m+n=39` and `m-3n=27` using substitution?

Answer 1

The solution for the system of equations is:
`color(green)(m = 9`
`color(green)(n =-6)`

Explanation:

`5m + n =39`..................equation `(1)`

`m - 3n = 27`
`color(green)(m = 27 + 3n`..................equation `(2)`

Substituting equation `(2)` in `(1)`

`5m + n =39`

`5 * (color(green)( 27 + 3n)) + n =39`

`5 * (color(green)( 27 )) + 5 * color(green)(( 3n)) + n =39`

`135 + 15n+ n =39`

`135 + 16n =39`

`16n =-96`

`n =-96/ (16)`

`color(green)(n =-6)`

Finding `m` by substituting the value of `n` in equation `(2)`:
`m = 27 + 3n`

`m = 27 + 3 * (-6)`

`m = 27 - 18`

`color(green)(m = 9`