# One number is seven less than a second number. Twice the first is 10 more than 6 times the second. How do you find the numbers?

Dec 6, 2016

The first number is $- 13$ and the second number is $- 6$

#### Explanation:

Let's let the first number be $n$ and the second number be called $m$.

Then, from the first sentence we can write:

$n = m - 7$

and from the second sentence we can write:

$2 n = 6 m + 10$

Substitute $m - 7$ for $n$ in the second equation and solve for $m$:

$2 \left(m - 7\right) = 6 m + 10$

$2 m - 14 = 6 m + 10$

$2 m - 14 - 2 m - 10 = 6 m + 10 - 2 m - 10$

$- 14 - 10 = 6 m - 2 m$

$- 24 = 4 m$

$\frac{- 24}{4} = \frac{4 m}{4}$

$m = - 6$

Now substitute $- 6$ for $m$ in the first equation and calculate $n$:

$n = - 6 - 7$

$n = - 13$