# Which are two numbers whose product is -60 and addition or subtraction is -17?

Jun 13, 2018

One solution is $\left(3 , - 20\right)$

Another solution is $\left(- 20 , 3\right)$

#### Explanation:

$x + y = - 17$

$x \cdot y = - 60$

Use substitution:

$x = - 17 - y$

$\left(- 17 - y\right) \cdot y = - 60$

$- 17 y - {y}^{2} = - 60$

${y}^{2} + 17 y - 60 = 0$

factor:

$\left(y + 20\right) \left(y - 3\right) = 0$

$y = - 20 \mathmr{and} y = 3$

solve $x$ values:

$x + y = - 17$

$x - 20 = - 17$

$x = 3$

One solution is $\left(3 , - 20\right)$

$x + 3 = - 17$

$x = - 20$

Another solution is $\left(- 20 , 3\right)$