top button
Flag Notify
    Connect to us
      Facebook Login
      Site Registration

Facebook Login
Site Registration

How many integer solutions are there to the system of following equations: x^2+y-z = 42; x+y^2-z = 18

0 votes

How many integer solutions are there to the system of equations below and which are those solutions?

x^2+y-z = 42
x+y^2-z = 18
posted Feb 26, 2017 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

1 Answer

0 votes

2 solutions- x=13, y=11 & x=6, y=2

If we subtract equations side-by-side,
x^2-y^2-x-y=24 --> (x+y)(x-y-1)=24, 24 can be shown as multiplication of 24*1 or 12*2 or 8*3 or 6*4 if we are looking for positive integer solutions.
then we have systems for each pair:
1. x+y=24, x-y-1=1--> x=13, y=1
2. x+y=12, x-y-1=2--> no integer solution
3. x+y=8, x-y-1=3--> x=6, y=2
4. x+y=6, x-y-1=4--> no integer solution

answer Jul 25, 2018 by Hanifa Mammadov

Similar Puzzles
Contact Us
+91 9880187415
#280, 3rd floor, 5th Main
6th Sector, HSR Layout
Karnataka INDIA.