Explanation

Let's directly evaluate the system of equations:

1x + 3y = 1

3x + λy = 3

For infinitely many solutions, these equations must represent the same line. Multiplying the first equation by 3 gives:

3x + 9y = 3

Comparing this with the second equation 3x + λy = 3, we see that λ must equal 9 for the equations to be identical.