Question

2/x+2/3y=1/6;3/x+3/y=0 solve this simultaneous equation

Answer 1

The answer is given below :

I think that the second equation has a mistake.

The given answer be helpful, if not see the attachment.

Given,

2/x + 2/(3y) = 1/6 .....(i)

and

3/x + 2/y = 0 .....(ii)

Now, from (ii), we get

3/x = -2/y

=> 1/x = -2/(3y) .....(iii)

Putting 1/x = -2/(3y) in (i), we get

2×{-2/(3y)} + 2/(3y) = 1/6

=> -4/(3y) + 2/(3y) = 1/6

=> (-4 + 2)/(3y) = 1/6

=> -2/(3y) = 1/6

=> 3y/(-2) = 6

=> y = 6 × (-2/3)

=> y = -4

Now, from (iii), we get

1/x = -2/{3×(-4)}

=> 1/x = (-2)/(-12)

=> 1/x = 1/6

=> x = 6

Therefore, the required solution be

x = 6 and y = -4

VERIFICATION :

When x = 6 and y = -4

Left Hand Side of (i) gives

= 2/6 + 2/{3 × (-4)}

= 1/3 - 1/6

= 1/6

= Right Hand Side of (i)

and

Left Hand Side of (ii)

= 3/6 + 2/(-4)

= 1/2 - 1/2

= 0

= Right Hand Side of (ii)

Thus, verified.

Thank you for your question.