Question

solve for x and y:  3/x-1/y+9=0, 2/x+3/y=5(x≠0,y≠0)

Answer 1

3/x-1/y=-9
2/x+3/y=5
multiplying eq1 by 3 and adding both eq.
9/x-3/y=-27
2/x+3/y=5
on adding we get,  11/x=-22   hence x=-1/2
puting x=  -1/2 in eq 1
3/(-1/2)+9=1/y
hence y=1/3

Answer 2

$\frac{3}{x} - \frac{1}{y} = -9 \\ \\ \frac{9}{x} - \frac{3}{y} = -27 ....(1) \\ \\ \frac{2}{x} + \frac{3}{y} = 5.....(2)$

Adding (1) and (2)
$\frac{11}{x} = -22 \\ \\ x = - \frac{11}{22} \\ \\ x = - \frac{1}{2}$

Substitute value of x in (2)
$\frac{2}{- (\frac{1}{2}) } + \frac{3}{y} = 5 \\ \\ -4 + \frac{3}{y} = 5 \\ \\ \frac{3}{y} = 9 \\ \\ y = \frac{3}{9} \\ \\ y = \frac{1}{3}$

Answer
$x = - \frac{1}{2} \\ \\ y = \frac{1}{3}$