Question 54435
L1) 4x-12y=5
L2) -x+3y=-1
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Solve L2) for x because that's the easiest one in which to isolate a variable.
-x+3y=-1
-x+3y-3y=-3y-1
-x=-3y-1
-(-x)=-(-3y-1)
x=3y+1
Substitute this value for x in L1) and solve for y.
4(3y+1)-12y=5
12y+4-12y=5
(12-12)y+4=5
0+4=5
4=5
We can't solve for y and 4 does not = 5, so this system is:{{{highlight(inconsistent)}}}.  It has no solution because the lines have no points in common.  Graphically, they would be parallel lines that never intersect.
If we got something that could not be solved for y but was true like 0=0 that would be dependent.
Happy Calculating!!!