How do you solve the system #y^2=x^2-9# and #2y=x-3#?

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Answer 1 · 2016-04-22T17:54:11

#{x=±5,y=4}#

#y^2=x^2-9#
#color(green)(y^2+9)=x^2" "(1)#

#2y=x-3#
#2y+3=x#
#color(green)((2y+3)^2)=x^2" "(2)#

#color(green)(y^2+9=color(green)((2y+3)^2))#

#y^2+9=4y^2+12y+9#

#4y^2-y^2+12y+9-9=0#

#3y^2+12y=0#

#cancel(3)cancel(y)^2=cancel(12)cancel(y)#

#y=4#

#"using (1)"#

#4^2+9=x^2#

#16+9=x^2#

#x^2=25#

#x=±5#

#{x=±5,y=4}#