beginner question about special relativity

[neginf]

Saw this in a book last night. I hope I read it right and am remembering it right.

If two rectangular coordinate systems share the same x axis and one is moving at a constant speed towards positive x and a beam of light is travelling along their x axes going towards the positive, then at the beam is at x=ct and x'=ct', one for each system.

The book says then x-ct=M(x'-ct') for some constant M.
What I don't get is doesn't x-ct=0=x'-ct' mean M is 1?

What am I not understanding about this?

[John232]

You can't add a variable to one side of an equation without adding it to both sides. A variable can end up being something other than one later on so that is why it is not done.

[ghwellsjr]

Saw this in a book last night. I hope I read it right and am remembering it right.

If two rectangular coordinate systems share the same x axis and one is moving at a constant speed towards positive x and a beam of light is travelling along their x axes going towards the positive, then at the beam is at x=ct and x'=ct', one for each system.

The book says then x-ct=M(x'-ct') for some constant M.
What I don't get is doesn't x-ct=0=x'-ct' mean M is 1?

What am I not understanding about this?
Why do you limit the solution to M=1?

M can be any value and the equation is still true, isn't it?

0 = M(0) is true for any value of M, correct?

[neginf]

Thank you both. x-ct=x'-ct'=0 so x-ct=anything*(x'-ct').