Question 54432
L1) x+5y=10
L2)-2x-10y=-20
--------------Multiply L1 by 2 so that if we add the two equations we eliminate the x's.
L1)2(x+5y)=2(10)------>2x+10y=20
---------------Add L1+L2
2x+10y=20
-2x-10y=-20
____________
0x+0y=0
0=0
This system is {{{highlight(dependent)}}} because we can't solve it and 0 does = 0.  This has an infinite number of solutions, no matter what we put in for their x's their y's will always =.  Graphically, it looks like the same exact line.
Happy Calculating!!!