Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
-x+3y=-1
4x-12y = 3
To determine the solution to the system of equations, we can solve the system by substitution or elimination. Let's solve it by elimination:
Multiply the first equation by 4 to make the x terms have the same coefficient:
-4x + 12y = -4
Now, write the second equation again:
4x - 12y = 3
Add the two equations together to eliminate the y terms:
(-4x + 12y) + (4x - 12y) = -4 + 3
-4x + 4x + 12y - 12y = -1
0 = -1
This equation shows a contradiction (0 = -1), which means the system of equations has no solutions.