Question #d8842

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Answer 1 · 2017-03-11T03:56:56

See the entire solution process below:

First, let's call the two numbers we are looking for $n$ $n$ and $m$ $m$ .

We can then write:

$n + m = 8$ $n + m = 8$

and

$n - m = 18$ $n - m = 18$

First, solve the second equation for $n$ $n$ :

$n - m + m = 18 + m$ $n - m + color(red)(m) = 18 + color(red)(m)$

$n - 0 = 18 + m$ $n - 0 = 18 + m$

$n = 18 + m$ $n = 18 + m$

Next, substitute $18 + m$ $18 + m$ for $n$ $n$ in the first equation and solve for $m$ $m$ :

$n + m = 8$ $n + m = 8$ becomes:

$(18 + m) + m = 8$ $(18 + m) + m = 8$

$18 + m + m = 8$ $18 + m + m = 8$

$18 + 2 m = 8$ $18 + 2m = 8$

$- 18 + 18 + 2 m = - 18 + 8$ $-color(red)(18) + 18 + 2m = -color(red)(18) + 8$

$0 + 2 m = - 10$ $0 + 2m = -10$

$2 m = - 10$ $2m = -10$

$\frac{2 m}{2} = - \frac{10}{2}$ $(2m)/color(red)(2) = -10/color(red)(2)$

$(color(red)(cancel(color(black)(2)))m)/cancel(color(red)(2)) = -5$

$m = -5$

Now, substitute $-5$ for $m$ in the solution to the second equation and calculate $n$ :

$n = 18 + m$ becomes:

$n = 18 + -5$

$n = 18 - 5$

$n = 13$

The two numbers are $13$ and $-5$