Question

Solve the pair of equations by reducing them to a pair of linear equations.
10/(x + y) + 2/(x - y) = 4
15/(x + y) - 5/(x - y) = -2

Answer 1

Hi ,

Let a = 1/( x + y ) ,

b = 1/( x - y ) ;

10/( x + y ) + 2/( x - y ) = 4

=> 10a + 2b = 4

=> 5a + b = 2

=> b = 2 - 5a ----( 1 )

15/( x + y ) - 5/( x - y ) = -2

=> 15a - 5b = -2---( 2 )

Substitute ( 1 ) in equation ( 2 ) , we get

15a - 5( 2 - 5a ) = -2

15a - 10 + 25a = -2

40a = -2 + 10

a = 8/40

a = 1/5

Substitute a = 1/5 in equation ( 1 )

we get,

b = 2 - 5 × ( 1/5 )

b = 2 - 1

b = 1

Therefore ,

1/( x + y ) = a = 1/5=> x + y = 5 -( 3)

1/( x - y ) = b = 1/1=> x - y = 1/1 --( 4 )

add equations ( 3 ) and ( 4 ), we get

2x = 5 + 1

2x = 6

x = 3

Substitute x = 3 in equation ( 3 ),

3 + y = 5

y = 5 - 3

y = 2

Therefore ,

x = 3

y = 2

I hope this helps you.

: )

Answer 2

     

                                       click this u will  get answer ok

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