Question

Multiplying to -5 adding to 4?

Answer 1

Xy = -5
x + y = 4

$xy = -5$
$\frac{xy}{x} = \frac{-5}{x}$
$y = \frac{-5}{x}$

$x + y = 4$
$x + \frac{-5}{x} = 4$
$\frac{x^{2}}{x} + \frac{-5}{x} = 4$
$\frac{x^{2} - 5}{x} = 4$
$x^{2} - 5 = 4x$
$x^{2} - 4x - 5 = 0$
$x^{2} - 5x + x - 5 = 0$
$x(x) - x(5) + 1(x) - 1(5) = 0$
$x(x - 5) + 1(x - 5) = 0$
$(x + 1)(x - 5) = 0$
$x + 1 = 0$    $or$    $x - 5 = 0$
$x = -1$    $or$    $x = 5$

   x + y = 4          or          x + y = 4
  -1 + y = 4          or          5 + y = 4
+ 1       + 1                     - 5        - 5
          y = 5             or             y = -1
    (x, y) = (-1, 5)               (x, y) = (5, -1)

The two numbers that add up to 4 and can multiply to -5 are -1 and 5.

Answer 2

5 and -1
5 x -1 = -5
5 + - 1 = 5 - 1 = 4