Question

solve for x and y 1/2x-1/y=-1 , 1/x+1/2y=8 (x≠0,y≠0)

Answer 1

Put $\frac{1}{x} = u, \frac{1}{y} = v$
Then,
$\frac{u}{2} - v = -1 , u + \frac{v}{2} = 8$

 2u - v = -2  . . . . . (1)
2u + v = 16  . . . . . (2)
Add the two equations
      4u = 14
        u = $\frac{7}{2}$
Substitute u in (1)
[tex]2( \frac{7}{2}) - v = -2 [/tex]
                        v = 7 + 2
                           = 9

x = $\frac{2}{7}$
y = $\frac{1}{9}$