Question

The value of 'k' for which the system of linear equations 6x + y = 3k and 36x + 6y = 3 have infinitely many solutions is ______.

Options

• 6

• `1/6`

• `1/2`

• `1/3`

Answer 1

The value of 'k' for which the system of linear equations 6x + y = 3k and 36x + 6y = 3 have infinitely many solutions is `bbunderline(1/6)`.

Explanation:

6x + y = 3k 
36x + 6y = 3     ....(i)

6x + y − 3k = 0
36x + 6y − 3 = 0         ....(ii)

For a system of two linear equations to have infinitely many solutions, ratios of coefficients of x, y and constant must be equal

∴ `6/36 = 1/6 = (-3k)/-3`

`6/36 = (-3k)/-3`

∴ `k = 1/6`