Question 1178330
<br>
x+y = -1
xy = -20<br>
Solve the first equation for one variable and substitute in the second equation.<br>
y = -1-x
x(-1-x) = -20
-x-x^2 = -20
x^2+x-20 = 0
(x+5)(x-4) = 0
x = -5 or x = 4<br>
If x = -5 then y = 4; if x = 4 then y = -5. Either way, the two numbers are -5 and 4.<br>
That's a nice exercise in using basic algebra to solve the problem. But using formal algebra on this problem is overkill.  Solve the problem using logical reasoning and simple mental arithmetic.<br>
The product of the two numbers is negative, so we know one is positive and one is negative.
Now ignore the signs for the moment; then we need two numbers whose product is 20 and whose difference is 1.  It takes about one second to find those numbers are 4 and 5.
Now make one of them positive and the other negative so that their sum is -1.<br>
ANSWERS: -5 and 4.<br>