for which value of k does the system x + y= 4; kx + y= 5 have no solutions?

Question

answer choices:

-1

1

4

5

Answer 1

Because systems only can have no solutions if they are parallel and because two lines are parallel if they have the same slope, the value of k must be the same as the coefficient in the other equation. Since we tend to assume that there is an invisible 1 in front of a variable if it's not written, k will also have to be a 1.