Find the valus of k for which the system of equations
` x - 2y = 3, 3 x + k y = 1 `
has a unique solution.

Options

A. `k!=6`
B. `k!=4`
C. `k!=8`
D. None

Answer

A

Explanation

The given system of equation is
` x - 2y - 3 = 0 , 3 x + ky - 1 = 0 `
These equations are of the form
` a_ 1 x + b _ 1 y + c_ 1 = 0 and a_ 2 x + b_ 2 y + c_ 2 = 0 `,
where ` a_ 1 , b_ 1 = - 2, c_ 1 = - 3 and a_ 2 = 3, b _ 2 = k, c _ 2 = - 1 `
For a unique solution, we must have ` (a_ 1 ) /(a_ 2) ne (b _ 1 ) /(b _ 2 )`
`therefore (1)/(3) ne (-2) /( k ) rArr k ne - 6 `
Hence, the given system of equations will have a unique solution for all real values of k, other than - 6.