Answer:
[tex]ax+ay=k; a\ne0, k\ne2a[/tex]; line D in the options.
Step-by-step explanation:
The set of equations has no solutions if the two lines are parallel. A quick way to create a parallel line is to solve for y, put it in slope-intercept form. Else, as long as the cofficient of x and y are in the same ratio (in this case 1:1), the two lines are parallel, you just have to be careful not to pick the same line again!
The condition [tex]a\ne 0[/tex] makes sure you are still getting lines (else you would get rid of both x and y); the condition [tex]k\ne 2a[/tex] makes sure you're not picking line A again, just written in a different form.
Now that we have the options:
A and C have a different ratio for the coefficient of x and y (2:1 and 1:2) so are not good.
Choice B is just a more complicated way to write the same line, you can see by dividing both sides by 2 and get back x+y=2.
Line D is correct.
