Question

How do you solve the system of equations `m-n=-9` and `7m+2n=9`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the first equation for `m`:

`m - n = -9`

`m - n + color(red)(n) = -9 + color(red)(n)`

`m - 0 = -9 + n`

`m = -9 + n`

Step 2) Substitute `(-9 + n)` for `m` in the second equation and solve for `n`:

`7m + 2n 9` becomes:

`7(-9 + n) + 2n = 9`

`(7 * -9) + (7 * n) + 2n = 9`

`-63 + 7n + 2n = 9`

`-63 + (7 + 2)n = 9`

`-63 + 9n = 9`

`color(red)(63) - 63 + 9n = color(red)(63) + 9`

`0 + 9n = 72`

`9n = 72`

`(9n)/color(red)(9) = 72/color(red)(9)`

`(color(red)(cancel(color(black)(9)))n)/cancel(color(red)(9)) = 8`

`n = 8`

Step 3) Substitute `8` for `n` in the solution to the first equation and the end of Step 1 and calculate `m`:

`m = -9 + n` becomes:

`m = -9 + 8`

`m = -1`

The Solution Is: `m = -1` and `n = 8`