Question

How do you solve the simultaneous equations `m+n=19` and `m-n=7` ?

Answer 1

`13` and `6`

Explanation:

Suppose the numbers are `m` and `n`.

We are given:

`{ (m+n=19), (m-n=7) :}`

Adding these two equations together we get:

`2m = 26`

Dividing both sides by `2`, we find:

`m=13`

Then from the first equation, we find:

`n = 19-m = 6`

Answer 2

See the entire solution process below:

Explanation:

First, let's define the two numbers we are looking for. I will call them:

`n` and `m`.

Next, from the problem we know we can write:

`n + m = 19` and `n - m = 7`

Then, solve the second equation for `n`;

`n - m = 7`

`n - m + color(red)(m) = 7 + color(red)(m)`

`n - 0 = 7 + m`

`n = 7 + m`

Now, substitute `7 + m` for `n` in the first equation and solve for `m`:

`n + m = 19` becomes:

`7 + m + m = 19`

`7 + 2m = 19`

`-color(red)(7) + 7 + 2m = -color(red)(7) + 19`

`0 + 2m = 12`

`2m = 12`

`(2m)/color(red)(2) = 12/color(red)(2)`

`(color(red)(cancel(color(black)(2)))m)/cancel(color(red)(2)) = 6`

`m = 6`

We have found the first number. To find the second number substitute `6` for `m` back into the equation we solved for `m` and calculate `n`:

`n = 7 + m` becomes:

`n = 7 + 6`

`n = 13`

The two numbers are `6` and `13`

`6 + 13 = 19` and `13 - 6 = 7`