# The sum of two numbers is 2 times their difference. The larger number is 6 more than twice the smaller. How do you find the numbers?

It is $\left(a , b\right) = \left(18 , 6\right)$

#### Explanation:

Let $a$ be the largest number
and $b$ the smallest number.

Hence we have that

$a + b = 2 \left(a - b\right) \implies a + b = 2 a - 2 b \implies a = 3 b$

and

$a = 6 + 2 b \implies 3 b = 6 + 2 b \implies b = 6$

and $a = 18$