Question

x-y=7
x2+y2=25
Sistema do segundo grau

Answer 1

x2+y2=25

 x+y= 7 ==> x = 7 - y

 (7-y)2+y2=25

  49 - 14y + y^2 + y^2 = 25

   2y^2 - 14y +49 - 25 = 0

   2y^2 - 14y + 24 = 0 (:2)

   y^2 - 7y + 12= 0

   delta = (-7)^2 -4.1.12= 49 - 24 = 25

  y = 7+/- V25 = 7+/- 5

             2.1             2

y1= 7+ 5 ==> y1= 6

         2

 y2= 7- 5 ==> y2= 1

         2

 x1 = 7 - y1 ==> x1 = 7 - 6 ==> x1 = 1

 x2 = 7 - y2 ==> x2 = 7 - 1 ==> x1 = 6