If x<0and y<0 x+y+x÷y=1÷2 and (x+y)x÷y=-1÷2 then find x and y?
1 Answer
Jun 7, 2018
# x = -1/4 # and#y=-1/4#
Explanation:
We have:
# x + y +x/y=1/2# ..... [A]
#(x+y)x/y=-1/2# ..... [B]
with
From [A] we have:
# x+y = 1/2-x/y #
Substituting into [B] we get:
#(1/2-x/y )x/y=-1/2#
Substitute
#(1/2-u )u=-1/2#
#:. u - 2u^2 = -1#
#:. 2u^2-u-1 = 0#
#:. (2u+1)(u-1) = 0#
Leading to two possible solutions:
# u = 1# or# u = -1/2#
We discard the negative solution as
# x + x +x/x=1/2#
# :. 2x+1 = 1/2 #
# :. x = -1/4 # and#y=-1/4#