Question

How do you solve `8m + n = 34` and `m - 4n = 29` using substitution?

Answer 1

The solution for the system of equations is:
`color(blue)(m=5`
`color(blue)(n = - 6`

Explanation:

`8m + n = 34`..............equation `(1)`

`m - 4n = 29`
`color(green)(m = 29 + 4n`..............equation `(2)`

Substituting equation `2` in `1`

`8m + n = 34`

`8 * (color(green)( 29 + 4n )) + n = 34`

`232 + 32n + n = 34`

`33n = 34 - 232`

`33n = - 198`

`n = - 198/33`

`color(blue)(n = - 6`

Finding `m` from equation `1`:
`8m + n = 34`

`8m = 34 - n`

`8m = 34 - (-6)`

`8m = 34 + 6`

`8m = 40`

`m = 40 / 8`

`color(blue)(m=5`