How do you find the exact solutions to the system #x^2/30+y^2/6=1# and #x=y#?

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Answer 1 · 2016-11-23T05:53:24

#x=y=-sqrt5# or #x=y=sqrt5#

#y^2/30+y^2/6=1#

#y^2/30xx30+y^2/6xx30=1xx30#

#y^2+5y^2=30#

#6y^2=30#

#y^2=30/6=5#

#y^2-5=0#

#(y+sqrt5)(y-sqrt5)=0#

Hence, either #y+sqrt5=0# i.e. #y=-sqrt5#

or #y-sqrt5=0# i.e. #y=sqrt5#

Hence, #x=y=-sqrt5# or #x=y=sqrt5#