SOLUTION: what numbers multiply to make -10 but add to make 5

So we have this system of two equations in two unknowns:



Solve the second one for y by subtracting x from both sides:



Substitute (5-x) for y in x∙y = -10



Get 0 on the right by adding 10 to both sides of the equation:



Get the left side in descending order:



Multiply through by -1 to make the leading term positive:
(Change all the signs):



That doesn't factor so we must use the quadratic formula:



a=1, b=-5, c=-10







So there are two solutions for x:

 and 

We find y for each solution using y=5-x

 and 

 and 

 and 

 and 

 and 

There really aren't two solutions, it's just a matter of which one
we call x and which one we call y.

Answer:  and  

Checking:

Multiply them: 







  <-- that checks!

Add them: 







  <-- that also checks!

Edwin