Question

##CHALLENGE FOR EVERYONE##
*LET'S SEE WHO CAN SOLVE THIS QUESTION*

Solve for x and y using substitution method:
$\frac{2x + 5y}{xy} = 6$
$\frac{4x - 5y}{xy} = - 3$
where x ≠ 0 and y ≠ 0.

Answer 1

2x+5y/xy = 6

so, 2x/xy + 5y/xy = 6
      2/y + 5/x = 6 .....................(1)

Similarly, 4/y - 5/x = -3 ..............(2)

Let 1/x = A and 1/y = B

So, We can write Eqn (1) and (2) as:

          2B + 5A = 6
      so, 5A = 6 - 2B ...........(3)

 and, 4B - 5A = -3

 so, By using Eqn (3) 
    4B - (6-2B) = -3
   4B -6 + 2B = -3
     6B = -3 + 6
    So, B = 3/6 = 1/2 

so, By putting B = 1/2 in Eqn (3)

 5A = 6 - 2(1/2)
5A = 6 - 1
5A = 5 
so, A = 1

Hence, 1/x = A so, x =1

 and 1/y = B so, y = 2


    

Answer 2

2x/xy + 5y/xy = 6 -------1equation

4x/xy - 5y/xy = -3. -----2equation

_________

In equation 1,

2/y + 5/x = 6

In equation 2,

4/y -5/x = -3


Now, let 1/x = a, 1/y =b

2b + 5a = 6.
4b - 5a = -3

6b = 3

b = 3/6

b =1/2

1/y = 1/2

y =2,

Putting the value of y in 1equation,


2/2 +5/x =6

1 +5x = 6

5x =6-1

x =5/5

x =1


I hope this will help you


-by ABHAY