#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}#