<PRE><B>Question 358829</B>
Dependent linear equations are ones which when simplified are the same equations.  Example: &lt;br&gt;

{{{x+y=5}}} and {{{2x+2y=10}}}&lt;br&gt;

Notice that both equations will have the same slope, and will also be the same line!  When this occurs, you will have an infinite number of solutions.&lt;br&gt;

Inconsistent linear equations are ones which when simplified are parallel lines, but are NOT the same line.  Example:&lt;br&gt;

{{{y=3x+1}}} and {{{y=3x-7}}}&lt;br&gt;

Notice that they do have the same slope, but have different y-intercepts, and thus, are totally different lines.  When this occurs, you will have no solutions!&lt;br&gt;

Independent linear equations are neither dependent nor inconsistent.  Example:&lt;br&gt;

{{{y=3x+1}}} and {{{y=-5x-7}}}&lt;br&gt;

When this occurs you will have one and only one solution.&lt;br&gt;

Simply put:&lt;br&gt;

Same slope, same y-intercept are dependent linear equations.&lt;br&gt;

Same slope, different y-intercept are inconsistent linear equations.&lt;br&gt;

Different slopes are independent linear equations.&lt;br&gt;

So check the slope, then the y-intercept and you will find out what kind of system of linear equations you are dealing with.&lt;br&gt;

I hope this helps!&lt;br&gt;</PRE>