Question

How do you solve 2m-5n=-6 and 2m-7n=-14?

Answer 1

`{(n=4), (m=7) :}`

Explanation:

Your system of equations looks like this

`{(2m - 5n = -6), (2m - 7n = -14) :}`

You can solve this by substituting `2m` from the first equation into the second equation and solving for `n`, or by multplying the first equation by `(-1)`, adding the resulting equation to the second equation, and then solving for `n`.

Here's how that first method would look.

`2m = - 6 + 5n`

`(-6 + 5m) - 7n = -14`

`5m - 7n = -14 + 6`

`-2n = -8 implies n = ((-8))/((-2)) = 4`

This means that `m` is equal to

`2m = -6 + 5 * (4)`

`m = 14/2 = 7`

The solution set will thus be

`{(n=4), (m = 7) :}`

Now try the second method.

`{(2m - 5n = -6 | (-1)), (2m - 7n = -14) :}`

`{(-2m + 5n = 6), (2m - 7n = -14) :}`
`stackrel("-------------------------------------------")`

`-color(red)(cancel(color(black)(2m))) + 5n + color(red)(cancel(color(black)(2m))) - 7n = 6 + (-14)`

`-2n = -8 implies n = 4`

Once again, `m = 7` and `n = 4`.