How do you find the exact solutions to the system #y^2=x^2-7# and #x^2+y^2=25#?

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Answer 1 · 2016-10-07T14:42:05

Let equation 1 be #y^2 = x^2 - 7# and equation #2# be #x^2 + y^2 = 25#.

We know the value of #y^2# in both equations, so we can substitute #y^2# in equation #1#, which is already isolated, for #y^2# in equation #2#.

#x^2 + (x^2 - 7) = 25#

#2x^2 = 32#

#x^2 = 16#

#x = +- 4#

#y^2 = 4^2 - 7" AND "y^2 = -4^2 - 7#

#y^2 = 9" AND "y^2 = 9#

#y = +-(3)" AND "y = +-(3)#

#:.#The solution is #(+-4, +-3)#

Hopefully this helps!