Question

2/x + 3/Y = 13 5/x - 4/Y = -2

Answer 1

Answer:

x = 1/2 , y = 1/3

Solution:

Here,

The given equations are :

2/x + 3/y = 13

5/x - 4/y = -2

Putting 1/x = a and 1/y = b in the given equations will reduce to linear equations .

Thus,

2a + 3b = 13 ---------(1)

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

Now,

Multiplying both sides of eq-(1) by 4 , we get ;

=> 4×(2a + 3b) = 13×4

=> 8a + 12b = 52 ---------(3)

Also,

Multiplying both sides of eq-(2) by 3 , we get ;

=> 3×(5a - 4b) = -2×3

=> 15a - 12b = -6 -------(4)

Now,

Adding eq-(3) and (4) , we get ;

=> 8a + 12b + 15a - 12b = 52 + (-6)

=> 8a + 15a = 52 - 6

=> 23a = 46

=> a = 46/23

=> a = 2

=> 1/x = 2 { °.° a = 1/x }

=> x = 1/2

Now,

Putting a = 2 in eq-(1) , we get ;

=> 2a + 3b = 13

=> 2×2 + 3b = 13

=> 4 + 3b = 13

=> 3b = 13 - 4

=> 3b = 9

=> b = 9/3

=> b = 3

=> 1/y = 3 { °.° b = 1/y }

=> y = 1/3

Hence ; x = 1/2 , y = 1/3