Question 970028
Use a substitution,
{{{A=1/(x+y)}}}
{{{B=1/(x-y)}}}
So then,
1.{{{40A+2B=5}}}
2.{{{25A-3B=1}}}
Multiply eq. 1 by 3 and eq. 2 by 2 and add them,
{{{120A+6B+50A-6B=15+2}}}
{{{170A=17}}}
{{{A=1/10}}}
So then,
{{{40/10+2B=5}}}
{{{4+2B=5}}}
{{{2B=1}}}
{{{B=1/2}}}
Substituting back,
{{{1/(x+y)=1/10}}}
3.{{{x+y=10}}}
.
.
{{{1/(x-y)=1/2}}}
4.{{{x-y=2}}}
Add eq. 3 to eq. 4,
{{{x+y+x-y=10+2}}}
{{{2x=12}}}
{{{x=6}}}
Then,
{{{6+y=10}}}
{{{y=4}}}