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

Options

A. 30
B. -10
C. 10
D. -30

Answer

3

Explanation

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`