SOLUTION: for what values of x will (x,y) be a solution of the system of the following equations x2+y2 = 25 both intergers are squared x+y=1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: for what values of x will (x,y) be a solution of the system of the following equations x2+y2 = 25 both intergers are squared x+y=1      Log On


   

Question 32397: for what values of x will (x,y) be a solution of the system of the following equations
x2+y2 = 25 both intergers are squared
x+y=1
Answer by mukhopadhyay(490) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=1 = > y = 1-x;
x^2+y^2 = 25
=> x^2 + (1-x)^2 = 25
=> 2x^2 - 2x + 1 = 25
=> 2x^2 - 2x - 24 = 0
=> x^2 - x - 12 = 0
=> (x-4)(x+3) = 0
=> x = 4 or x = -3
If x=4, y = 1-x = -3;
If x=-3, y = 1-x = 4
Answer: (x,y) belongs to {(4,-3), (-3,4)}