Question

10/x+y+2/x-y=4; 15/x+y-5/x-y=-2 Solve the simultaneous equation

Answer 1

SOLUTION IS IN THE ATTACHMENT..

Sometimes equation are not linear but they can be reduced to a pair of linear equation by making some suitable substitutions.
•if the given equation involves 1/(x+y), 1/(x-y) , then put 1/(x+y)= p and 1/(x -y) = q to convert them into linear form. After solving, put the values of p and q in above substitutions , to get linear equations in x and y. Now solve these equations to get the value of x and y.

HOPE THIS WILL HELP YOU….

Answer 2

Given equations are ,

10/( x + y ) + 2/( x - y ) = 4 ---( 1 )

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

Let ,

1/(x+y) = a , 1/(x-y) = b

10a + 2b = 4

Divide each term with 2 , we get

5a + b = 2

=> b = 2 - 5a ----( 3 )

15a - 5b = -2 -----( 4 )

Substitute b = 2 - 5a in equation

( 4 ) , we get

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

=> 15a - 10 + 25a = -2

=> 40a = -2 + 10

=> 40a = 8

=> a = 8/40

=> a = 1/5

Put a = 1/5 in equation ( 3 ) , we

get

b = 2 - 5 × 1/5

=> b = 2 - 1

b = 1

Therefore ,

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

1/(x-y) = 1/1 => x - y = 1 ---( 6 )

Add equations ( 5 ) and ( 6 ) ,

We get

2x = 6

=> x = 6/2 = 3 ,

Put x = 3 in equation ( 5 ) , we get

3 + y = 5

=> y = 5 - 3 = 2

Therefore ,

x = 3 , y = 2

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