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.
