Find the value of k for which the system of equations
` 3x + 5y = 0 , k x + 10 y = 0 `
has a nonzero solution.

Options

A. `k=6`
B. `k=5`
C. `k=4`
D. `k=3`

Answer

A

Explanation

The given equations are of the form
` a_ 1 x + b_ 1 y = 0 and a_ 2 x + b_ 2 y = 0 `
where ` a_ 1 = 3, b_1 = 5 and a_ 2 = k ,b_ 2 = 10 `
Then , `(a _ 1 ) /( a _ 2) = (3) /( k ) and (b_ 1 ) /(b_ 2) = ( 5) /(10) = (1)/(2)`
Let the given system of equations have a nonzero solution.
Then, ` (a_ 1 ) /(a _ 2 ) = (b _ 1 ) /(b _ 2 ) rArr ( 3) /(k ) = (1)/(2) rArr k = 6 `
Hence, the required value of k is 6.