Question 103927
Let's say you have the two equations {{{y=2x+1}}} and {{{2y=4x+2}}}. If you divide both sides of {{{2y=4x+2}}} by 2 you get {{{y=2x+1}}} (which is the same equation as the first one)



Now set the two equations equal to each other


{{{2x+1=2x+1}}}



{{{2x+1-2x=1}}} Subtract 2x from both sides



{{{2x-2x=1-1}}} Subtract 1 from both sides



{{{0=0}}} Subtract



So if you set one side of an equation equal to itself, then you get the identity {{{0=0}}}. This means that any x value will satisfy the equation {{{y=2x+1}}}. So there are an infinite number of solutions and the system is dependent (since the second equation is dependent on the first one)