Question 116145
The point at which two linear equations intersect represents the solution to the system of equations. The solution solves both equations simultaneously. 
As an example, 
{{{-2x+y=1}}}
{{{x-y=1}}}
{{{ graph( 300, 200, -5, 5, -5, 5, 2x+1, x-1) }}} 
For this system of equations, there is a solution (independent, consistent).
The solution is x=-2, y=-3. 
If there is no solution, the case is either that the linear equations represent the same line (dependent).
{{{2x+y=1}}}
{{{6x+3y=3}}}
{{{ graph( 300, 200, -5, 5, -5, 5, 1-2x, (3-6x)/3) }}} 
 or the lines are parallel and never meet (inconsistent). 
{{{2x+y=1}}}
{{{2x+y=7}}}
{{{ graph( 300, 200, -5, 5, -5, 5, 1-2x, 7-2x) }}}