Algebra.Com's Answer #101487 by solver91311(24713)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
I suspect you are actually referring to a SYSTEM of equationS. \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Let's say you have a system of equations like this:\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "
\n" );
document.write( " \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "If for any real number  ,  AND  AND  , then you have a system with infinitely many solutions. That is to say that the two equations graph to exactly the same line.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "If for any real number , AND AND  , then you have a system with no solutions. That is to say that the two equations graph to two parallel lines. The fact that the coefficients on the x and y terms are proportional means that the slope of the two lines is equal, but the fact that the constant terms are not proportional means that the two lines have different y-intercepts.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "If for any real number ,  OR  , then you have a system with exactly one solution. That is to say that the two equations graph to two lines that intersect in a single point.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "If you don't mean a system of equations, then you are perhaps talking about a situation where the equation reduces to a trivial identity, such as  , then the original relationship is always true no matter what value you select for the variable (presuming the selected value is in the domain of the function in the first place). This situation means that there are infinitely many solutions. On the other hand, if you have something that reduces to an absurdity, such as  , then you have a situation where NO value substituted for the variable in the original relationship will make the relationship true, hence there are no solutions.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Examples:  =>  =>  =>  . Always true for any value of x, infinite elements in the solution set.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " =>  =>  Absurd. No value of the variable can make the given relationship a true statement. The solution set is the empty set.\r
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |