Question

Solve the following pair of equations by reducing them to a pair of linear equation-

7/x + 8/y = 2
1/x + 6/y = 10​

Answer 1

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7/x+y=2×8

7/x+y=16

x+y=16×7

anzss..x+y=112

Answer 2

let we take 1/x=u,1/y=v

7u+8v=2--------1

1u+6v=10-------2

then we multiple 1 in equation 1 & 7 in equation 2,

1 *=7u +8v=2

7*=1u+ 6v=10

we get,

7u +8v =2-------3

& 7u +42v =70-------4

now subtract equation 4 from 3 , we get

7u+42v=70

7u+8v=2

(-)______________

34v=68 (7u &7u are cancelout)

v =68/34

v= 2

now, put the value of 'v' in equation 3,

7u+8v=2

7u +8(2)=2

7u+16=2

7u=2-16

7u=-14

u=-14/7

u=-2

but we have to find x &ym y

we know that, u=1/x--------5

v=1/y---------6

now put the value of u & v in equation 5 & 6

u=1/x v=1/y

-2=1/x 2=1/y

x=-2 y=2

so the value of x & y are

x=-2

y=2

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