How many solutions does this system have. -3x + 6y= 10 and -3x + 6y=-4
None, one, infinite or two?
I think it's infinite but not sure

Question

How many solutions does this system have. -3x + 6y= 10 and -3x + 6y=-4
None, one, infinite or two?
I think it's infinite but not sure

campbell_st · Answer

the lines are parallel.. so don't intersect... hence no solutions

write them in slope intercept for and its 

y = 1/2 x + 10/6     and  y = 1/2 x - 4/6

hope this helps

anonymous · Answer

Thanks, it does. I will rework to get my x and y.

campbell_st · Answer

you don't have to rework anything...other than showing there are parallel....same slope

different y- intercepts..

anonymous · Answer

Also you can see that there is no solution from inspection, that is, the same expression is on the LHS of both equations but two different expressions are on the RHS. Also you can fint the determinant of the matrix $$\left[\begin{matrix}-3 & 6 \ -3 & 6\end{matrix}\right]$$ and see that it is equal to zero which means 1 of two things, either there is an infinitely many or no solution.