Question

Solve the pair of equations by reducing them to a pair of linear equations.
5/(x - 1) + 1/(y - 2) = 2
6/(x - 1) - 3/(y - 2) = 1

Answer 1

Hi ,

Let 1/( x - 1 ) = a ,

1/( y - 2 ) = b ,

5/(x-1) + 1/(y-2) = 2 => 5a + b = 2 --( 1 )

6/(x - 1 )-3/(y-2) = 1 =>6a - 3b = 1 ---( 2 )


Do [ ( 1 ) × 3 + ( 2 )] , we get

15a + 3b = 6

6a - 3b = 1
__________

21a = 7

a = 7/21

a = 1/3

Substitute a = 1/3 in equation ( 2 ),

we get

6 × ( 1/3 ) - 3b = 1

=> 2 - 3b = 1

=> -3b = -1

b = 1/3

Therefore ,

1/( x - 1 ) = a = 1/3

=> x - 1= 3

=> x = 4

1/( y - 2 ) = b = 1/3

=> y - 2 = 3

y = 5

Therefore ,

x = 4 , y = 5

I hope this helps you.

: )

Answer 2

HELLO DEAR,

GIVEN:-

5/(x - 1) + 1/(y - 2) = 2 ,

6/(x - 1) - 3/(y - 2) = 1

[put 1/(x - 1) = p , 1/(y - 2) = q]

therefore,

5p + q = 2------------( 1 )

6p - 3q = 1------------( 2 )

from--------( 1 ) & ---------( 2 )

multiply-------( 1 ) by "3"

so,

15p + 3q = 6

6p - 3q = 1

———––––––—

21p = 7

p = 1/3 [ put in ------( 1 )]

we get,

5p + q = 2

5(1/3) + q = 2

(5 + 3q)/3 = 2

5 + 3q = 6

3q = 6 - 5 = 1

q = 1/3

now,

p = 1/(x - 1) = 1/3

x - 1 = 3

x = 4

AND,

q = 1/(y - 2) = 1/3

y - 2 = 3

y = 5 , x = 4

I HOPE ITS HELP YOU DEAR,

THANKS