Question

please solve this 18th by Elimination by equating Coefficients method.

Answer 1

Take 1/(x+y) = X and 1/(x-y) = Y
Then solve for X and Y and find solutions of X and Y
Now pu these values in our assumption and solve again for X and y .

Answer 2

Lets assume
$\frac{1}{x+y} = X and \frac{1}{x-y} = Y$

Now, the both equation becomes,
5X-2Y= -1 and.............(i)
15X+7Y=10...................(ii)

performing (ii) - 3(i),  we get
13Y=13
Y=1, substituting in (i) we get
X=1/5

therefore
$\frac{1}{x+y} = \frac{1}{5} and \frac{1}{x-y} = 1$

so
x+y=5 and.....................(iii)
x-y=1...............................(iv)
 
adding eq (iii) and (iv) we get
2x=6
x=3
and by substituting x=3 in (iii) we get
y=2

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