Question

27/x-2+31/y+3=85; 31/x-2+27/y+3=89 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±a, 1/y±b , then put 1/(x±a)= p and 1/(y±b)= q to convert them into linear form. After solving, put the values of p and q in above substitutions ,to get the value of x and y.

HOPE THIS WILL HELP YOU….

Answer 2

Given equations are ,

27/(x-2) + 31/(y+3) = 85 --( 1 )

31/(x-2) + 27/(y+3) = 89 ---( 2 )

Let 1/(x-2) = a , 1/(y+3) = b

27a + 31b = 85 ---( 3 )

31a + 27b = 89 ---( 4 )

Do [ 31×(3) - 27×(4) ] , we get

961b - 729b = 2635 - 2403

=> 232b = 232

=> b = 232/232

b = 1 ,

Substitute b = 1 in equation (3),

We get

27a + 31 = 85

=> 27a = 85 - 31

=> 27a = 54

=> a = 54/27

a = 2 ,

Therefore ,

1/(x-2) = a = 2/1

=> 2(x-2) = 1

=> 2x - 4 = 1

=> 2x = 5

=> x = 5/2 = 2.5

And ,

1/(y+3) = b = 1

=> y + 3 = 1

=> y = -2

Therefore ,

x = 2.5 , y = -2

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