does the system have one solution, no solution, or an infinite number of solutions?
5x-y=10
x+6y=33
a. one b. infinite numbers c. none

Question

anonymous · Answer

well its not c, you can use substitution and find one answer so a

anonymous · Answer

it certainly doesn't have infinite solutions. it has to be either one or none.

anonymous · Answer

ok so i had answered none on my exam and ur saying infinite number cant be it so it definetly has to be one. thanks a bunch

anonymous · Answer

Both of those functions are linear (lines). 
They will have no solution if and only if they are parallel. 
They will have infinite solutions if they are the same line. 
If neither of those is the case then they will intersect at exactly one point.

anonymous · Answer

You can see that they are not parallel because -5 (the slope of the first equation) does not equal 1/6 (the slope of the second equation). Therefore they cannot be the same line (as that would of course have the same slope). Thus they have 1 solution.

anonymous · Answer

awesomeness generously explained thank you