SOLUTION: The sum of x and y is 4 and the product xy is -32. Find x and y.

Algebra ->  Equations -> SOLUTION: The sum of x and y is 4 and the product xy is -32. Find x and y.      Log On


   



Question 212939: The sum of x and y is 4 and the product xy is -32. Find x and y.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1). x%2By+=+4 "The sum of two numbers is 4..."
2). x%2Ay+-+-32 "...the product xy is -2.
Rewrite equation 1 as: x+=+4-y and substitute into equation 2 then solve for y.
2a) %284-y%29%2Ay+=+-32 Simplify.
2b) 4y-y%5E2+=+-32 Rearrange into standard quadratic form.
2c) y%5E2-4y-42+=+0 Factor the trinomial.
2d) %28y-8%29%28y%2B4%29+=+0
2e) y+=+8 or y+=+-4
From equation 1:
x%2By+=+4
x%2B8+=+4
x+=+-4
The two numbers are:
x+=+-4 and y+=+8 or x+=+8 and y+=+-4 Both pairs will work.