# Two numbers add to 13 and multiply to 42. What are the two numbers?

Sep 1, 2016

The numbers are $6$ and $7$.

#### Explanation:

Let the first number be $x$ and the second be $y$.

$x + y = 13$

$x y = 42$

$y = 13 - x$

$x \left(13 - x\right) = 42$

$13 x - {x}^{2} = 42$

$0 = {x}^{2} - 13 x + 42$

$0 = \left(x - 7\right) \left(x - 6\right)$

$x = 7 \mathmr{and} 6$

$\therefore$ The numbers are $7$ and $6$.

Hopefully this helps!