Question 120712
The answer to this question will sometimes vary depending on which area of mathematics you are considering. However, in general:
if you get a result such as 0=0, this implies a true statement, and as such is the case, any value of a particular variable will work.

Example: Consider this system of equations:
          {{{2x+y=1}}}
         {{{4x+2y=2}}}

If we solve the first equation for y, we get {{{y=-2x+1}}},
now substituting this y into the second equation,

{{{4x+2(-2x+1)=2}}}
as you can see, we will get the statement {{{2=2}}}. Thus, {{{y=-2x+1}}} gives us a y value for any x that we can choose. Moreover, y is the dependent variable.

On the other hand, you can sometimes get a result such as {{{0=1}}}, which is a false statement. This implies that there is no solution to an equation or a system of equations.

Example: Consider this system of equations: 
            {{{x+y=1}}}
            {{{x+y=-1}}}
Solve for y in the first equation: {{{y=-x+1}}}
substitute this into the second equation: {{{x+(-x+1)=-1}}}. As you can see, this will result in the statement that {{{1=-1}}} which is false, there are no values of x or y that make that system true.