Which Coefficient will Make a 2-Variable Linear System Solvable? This is most likely a pretty simple problem although my textbook doesn't quite explain how to solve it. I have a linear system with two equations and two variables (x and y) below:
2x - 5y = 9

4x + ay = 5 ('a' being the unknown coefficient of y)

The question asks to find the value of a that will make this system have a single solution. At first this seemed trivial, although I tried 1) multiplying the top equation by -2 and then adding the two equations to eliminate x. I then got stuck at 10y + ay = -4. And 2) I tried only multiplying the top by 2 to get the 4x terms in both equations, in which case I thought that I could somehow remove the x terms out of both equations entirely but I don't think that's correct (unless I do it to both sides which doesn't help me much?). Thanks in advance for any help!
I also wasn't able to think of any suitable tags for this question except "systems of equations" (which is supposed to be used on conjunction with a more specific tag). Couldn't find "linear equations" or other more suited tags.

The only thing that would keep the system from yielding a single value is if $2a+20=0$ or $a=-10$. In that case the loci of the two equations would be parallel. No intersections means no solutions.
