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If the system of linear equations x+ky...

If the system of linear equations x+ky+3z=0 3x+ky-2z=0 2x+4y-3z=0 has a non-zero solution (x,y,z) then `(xz)/(y^2)` is equal to

A

30

B

-10

C

10

D

-30

Text Solution

Verified by Experts

The correct Answer is:
3
Given system of equations
`x+ky+3z=0`
`3x+ky -2x =0`
`2x+4y -3z =0`
Eliminating from first two equations we get
`2x-5z=0 " or " 2x=5z`
` :. X=5lambda , z= 2lambda`
from equation (iii) we have
`10 lambda +4y-6lambda= 0 " or " y=-lambda`
`:. (xz)/(y^(2)) =((5lambda)(2lambda))/((-lambda)^(2)) =10`
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