Question 325941
<pre><b>
{{{system(2/x-3/y= -11/10,
3/x+1/y= 11/10)}}}

Important: 
When all variables occur only as denominators, then
DO NOT CLEAR OF FRACTIONS!!!.  Instead leave the fractions and
use elimination:

To eliminate y, multiply the second equation through by 3

{{{system(2/x-3/y= -11/10,
9/x+3/y= 33/10)}}}

Add corresponding terms:

{{{system(2/x-cross(3/y)= -11/10,
          9/x+cross(3/y)= 33/10)}}}

{{{11/x}}}{{{""=""}}}{{{22/10}}}

Take reciprocals of both sides:

{{{x/11}}}{{{""=""}}}{{{10/22}}}

Multiply both sides by 11

{{{ll*""}}}{{{x/11}}}{{{""=""}}}{{{11*""}}}{{{10/22}}}

{{{cross(ll)*""}}}{{{x/cross(11)}}}{{{""=""}}}{{{cross(11)*""}}}{{{10/(""^2cross(22))}}}

{{{x}}}{{{""=""}}}{{{10/2}}}

{{{x}}}{{{""=""}}}{{{5}}}

Now substitute {{{5}}} for {{{x}}} in one of the original
equations:

{{{2/x-3/y}}}{{{""=""}}}{{{-11/10}}}

{{{2/5-3/y}}}{{{""=""}}}{{{-11/10}}}

NOW it is OK to clear of fractions,
Multiply through by 10y:

{{{10y*""}}}{{{2/5}}}{{{-10y*""}}}{{{3/y}}}{{{""=""}}}{{{10y*""}}}{{{-11/10}}}

{{{""^2cross(10)y*""}}}{{{2/cross(5)}}}{{{-10cross(y)*""}}}{{{3/cross(y)}}}{{{""=""}}}{{{cross(10)y*""}}}{{{-11/cross(10)}}}

{{{4y}}}{{{-30}}}{{{""=""}}}{{{-11y}}}

{{{15y}}}{{{""=""}}}{{{30}}}

{{{y}}}{{{""=""}}}{{{2}}}

Edwin</pre>