How solve system 1/(x-y)-1/(x+y)=1, 1/(x-y)+1/(x+y)=2 ? don't eliminate x,y

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The given equations can be solved by the method of substitution as follows:

`1/(x-y)-1/(x+y)=1` .............(i) and

`1/(x-y)+1/(x+y)=2` ..............(ii)

From eqn (i), `1/(x-y)=1+1/(x+y)`

Substitute this value in eqn. (ii),

`1+1/(x+y)+1/(x+y)=2`

`rArr 2/(x+y)=2-1`

`rArr x+y=2` --- (iii)

Again substitute this value of (x+y) in eqn. (i),

`1/(x-y)-1/2=1`

`rArr 1/(x-y)=1+1/2=3/2`

`rArr x-y=2/3` --- (iv)

Again, from eqn. (iii), it follows that x=(2-y)

substitute this value of x in eqn. (iv),

`2-y-y=2/3`

`rArr 2(1-y)=2/3`

`1-y=1/3`

`rArr y=1-1/3=2/3`

and, `x=2-2/3=4/3`

**Therefore, solving the given equations by the method of substitution yields x=4/3, y=2/3.**

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