Question

reduce the pair of equations 4/x+3/y=-2; 5/x +2/y=13​

Answer 1

Question:

Reduce the pair of equations 4/x + 3/y = 2 &

5/x + 2/y = 13 and find the solution.

Answer:

x = 1/5 , y = -1/6

Solution:

The given pair of linear equations are ;

4/x + 3/y = 2 -------(1)

5/x + 2/y = 13 ------(2)

Now,

Let 1/x = a and 1/y = b and substituting these values in eq-(1) and (2) , they will be reduced to ;

4a + 3b = 2 -----(3)

5a + 2b = 13 -----(4)

Now,

Multiplying eq-(3) both the sides by 2 , we have ;

=> 2•(4a + 3b) = 2•2

=> 2•4a + 2•3b = 4

=> 8a + 6b = 4 ---------(5)

Now,

Multiplying eq-(4) both the sides by 3 , we have ;

=> 3•(5a + 2b) = 13•3

=> 3•5a + 3•2b = 39

=> 15a + 6b = 39 -------(6)

Now,

Subtracting eq-(5) from eq-(6) , we have ;

=> (15a + 6b) - (8a + 6b) = 39 - 4

=> 15a + 6b - 8a - 6b = 35

=> 7a = 35

=> a = 35/7

=> a = 5

=> 1/x = 5 { since , 1/x = a }

=> x = 1/5

Now,

Putting a = 5 in eq-(3) , we have ;

=> 4a + 3b = 2

=> 4•5 + 3b = 2

=> 20 + 3b = 2

=> 3b = 2 - 20

=> 3b = - 18

=> b = - 18/3

=> b = - 6

=> 1/y = -6. { since , 1/y = b }

=> y = -1/6

Hence,

The required solution for the given pair of equations is ; x = 1/5 , y = -1/6 .