Question 245229
Write equations for each phrase
;
"Two numbers differ by 8,
x - y = 8
or
x = y + 8
:
 the sum of their squares is 320. 
x^2 + y^2 = 320
:
Replace x with (y+8)
(y+8)^2 + y^2 = 320
:
FOIL
y^2 + 16y + 64 + y^2 = 320
:
A quadratic equation
2y^2 + 16y + 64 - 320 = 0
2y^2 + 16y - 256 = 0
:
Simplify, divide by 2
y^2 + 8y - 128 = 0
Factor
(y+16)(y-8) = 0
:
Two solutions
y = 8, then x = 16
Or
y = -16 then x = -8