Question

Solve this linear equation please tomorrow is my exam
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Answer 1

Question

$\sf \dfrac{5}{x + y} + \dfrac{3}{x - y} = 4$

$\sf \dfrac{2}{x + y} + \dfrac{5}{x + y} = 5\ \dfrac{2}{5}$

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Let 1/x+y be 'u' and 1 / x-y be 'v'

our Equation become:

=>5u +3v=4---× 2

=>2u+5v= 27/5-----×5

Our new Equation obtained:

10u +6v=8

10u+25v=27

$(-)\:(-)\:\:(-)$

_______________

-19v=-19

v= 1

Now,put v's value into this equation to obtain I'd value

=>5u+3v=4

=>5u +3= 4

=>5u= 1

=>u=1/5

u=1/5

Now,we have let 1/x+y = u & 1/x-y= v

Now , equate the term

=>1/x+y= 1/5

=>5= x+y ---(1)

=>1/x-y= v

=>1/x-y= 1

=>x-y= 1----(2)

Adding Equation 1 and 2

=>x+y+x-y=6

=>2x=6

=>x=3

=>5=x+y

=>5= 3+y

=>y=2

we get x= 3 & y= 2