Question

solve 57/x+y +6/x-y =5 and 38/x+y + 21/x-y =9​

Answer 1

Answer:

Step-by-step explanation:

given that

57/x+y     +     6/x-y  =  5

38/x+y    +      21/x-y  = 9

let , 1/x+y  = a    - - - - -(i)

and ,  1/ x-y = b  - - - - - (ii)

∴, the equations become

57a + 6b = 5  - - - - - - -(iii)

38a + 21b = 9 - - - - - - - -(iv)

multiply eq (iii) by 7 , we get

399a + 42b = 35 - - - - - -(v)

multiply eq (iv) by 2 , we get

76a + 42b = 18  - -  - - - -(vi)

subtract eq(vi) from eq(v),we get

323a = 17

⇒ a = 1/19 - - - -- - - -(vii)

putting the value of a in eq(vi),weget

42b + 76(1/19) = 18

42b + 4 = 18

42b = 14

⇒ b = 1/3 - - - - - -(viii)

   

putting value of a from eq (vii) , to eq(i), we get

1/x+y = 1/19

⇒x + y = 19 - - - - -(ix)

putting value of b frome eq(viii) , to eq(ii), we get

1/x-y = 1/3

⇒x-y = 3 - - - - - -(x)

add eq (ix) and eq (x) , we get

2x = 16

x = 8

subtract eq (x) from eq(ix), we get

2y = 16

y = 8

therefore the value of x and y in the given equation is 8 and 8 respectively

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