document.write( "Question 116145: When graphing two linear equations, what is the signifiance of the intersection of the two graphs. ans if there is no intersection? \n" ); document.write( "

Algebra.Com's Answer #84461 by Fombitz(32388) $\"\"$ $\"About$

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The point at which two linear equations intersect represents the solution to the system of equations. The solution solves both equations simultaneously.
\n" ); document.write( "As an example,
\n" ); document.write( " $\"-2x%2By=1\"$
\n" ); document.write( " $\"x-y=1\"$
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+2x%2B1%2C+x-1%29+\"$
\n" ); document.write( "For this system of equations, there is a solution (independent, consistent).
\n" ); document.write( "The solution is x=-2, y=-3.
\n" ); document.write( "If there is no solution, the case is either that the linear equations represent the same line (dependent).
\n" ); document.write( " $\"2x%2By=1\"$
\n" ); document.write( " $\"6x%2B3y=3\"$
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+1-2x%2C+%283-6x%29%2F3%29+\"$
\n" ); document.write( " or the lines are parallel and never meet (inconsistent).
\n" ); document.write( " $\"2x%2By=1\"$
\n" ); document.write( " $\"2x%2By=7\"$
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+1-2x%2C+7-2x%29+\"$ \n" ); document.write( "

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