# 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#