Question

Solve: $\frac{2}{x}+\frac{3}{3y}=\frac{1}{6}$ and $\frac{3}{x}+\frac{2}{y}=0$, where $x\ne 0;y\ne 0$.

Answer 1

$\frac{2}{x}+\frac{3}{3y}=\frac{1}{6}$ , $\frac{3}{x}+\frac{2}{y}=0$

$\frac{1}{x}=u,\frac{1}{y}=v$

$2u+v=\frac{1}{6}$.....(i)

$3u+2v=0$.....(ii)

multiply (i) by 2 and substract it from (ii)

$3u+2v=0$

$4u+2v=1/3$

$---$

______________

$-u=-1/3$

$u=1/3,v=-1/2$

$\therefore x=3,y=-2$