Question

5/x-1+1/y-2=2 and 6/x-1 - 3/y-2 = 1

Answer 1

To Find:

Value of x and y=?

Solution:

5/x-1+1/y-2=2..........(1)

6/x-1-3/y-2=1.............(2)

Replacing 1/x-1 by a and 1/y-2 by b we get,

5a+b=2.................(3)

6a-3b=1...................(4)

Multiplying equation (3) by 3 we get,

15a+3b=6...........(5)

Adding equations (4) and (5) we get,

21a=7

a=7/21

a=1/3.

Substituting the value of a in equation (3) we get,

5(1/3) +b=2

5/3+b=2

b=2-5/3

b=6-5/3

b=1/3

Now, 1/x-1=a

→ 1/x-1=1/3

→ 1×3=x-1

→3=x-1

→ x=3+1

→ x=4

and, 1/y-2=b

1/y-2=1/3

1×3=y-2

3=y-2

y=3+2

y=5

So, (4, 5) Are the roots of the equations......