How do you find the exact solutions to the system #x^2+y^2=64# and #x^2+64y^2=64#?

Question

4301 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-10T23:42:57

Please see the explanation for steps leading to the points #(-8, 0) and (8,0)#

Given:

#x^2 + y^2 = 64" [1]"#
#x^2 + 64y^2 = 64" [2]"#

Subtract equation [1] from equation [2]:

#63y^2 = 0#

#y = 0#

#x^2 = 64#

#x = +-8#

The solutions are the points #(-8, 0) and (8,0)#