Question

Solve for x and y:

$\frac{3}{x}-\frac{1}{y}+9=0,\frac{2}{x}+\frac{3}{y}=5(x\ne 0,y\ne 0).$

Answer 1

3/x−1/y+9=0......(1)

2/x+3/y=5
2/x+3/y-5=0.....(2)

multiply by 3 in (1)
9/x-3/y+27=0

add this with (2) we get
(2/x+9/x)+(-5+27)=0
11/x+22=0
11/x=-22
11/-22=x
x=-1/2 put in (1)
3/(-1/2)-1/y+9=0
-6-1/y+9=0
3=1/y
y=1/3

so x=-1/2 and y=1/3