document.write( "Question 1023756: linear equations with substitution and graphing-
\n" ); document.write( "3x-y=2
\n" ); document.write( "-6x+2y=6 \n" ); document.write( "
Algebra.Com's Answer #639330 by KMST(5328)\"\" \"About 
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Substitution:
\n" ); document.write( "\"3x-y=2\"-->\"3x-2=y\"
\n" ); document.write( "Substituting the expression \"3x-2\" for \"y\" in \"-6x%2B2y=6\" we get
\n" ); document.write( "\"-6x%2B2%283x-2%29=6\"-->\"-6x%2B6x-4=6\"--->\"-4=6\"
\n" ); document.write( "Since \"-4=6\" is not true for any pair of (x,y) values,
\n" ); document.write( "the system has no solution.
\n" ); document.write( "It is \"inconsistent\".
\n" ); document.write( "Of course, you could also have simplified the second equation:
\n" ); document.write( "\"-6x%2B2y=6\"-->\"%28-6x%2B2y%29%2F2=6%2F2\"-->\"-3x%2By=3\" , or
\n" ); document.write( "\"-6x%2B2y=6\"-->\"%28-6x%2B2y%29%2F%28-2%29=6%2F%28-2%29\"-->\"3x-y=-3\" , which would have shown the system is inconsistent,
\n" ); document.write( "because \"3x-2y\" cannot be equal to \"2\" and to \"-3\" at the same time.\r
\n" ); document.write( "\n" ); document.write( "Graphing:
\n" ); document.write( "\"3x-y=2\" obviously passes through point (0,-2),
\n" ); document.write( "because when \"x=0\" , \"3x-y=-y=2\" .
\n" ); document.write( "When \"y=1\" , \"3x-1=2\"-->\"3x=2%2B1\"-->\"3x=3\"-->\"x=1\" ,
\n" ); document.write( "so \"3x-y=2\" also passes through point (1,1).
\n" ); document.write( "Plotting points (0,-2) and (1,1), and connecting them with a straight line we get the graph for \"3x-y=2\" .
\n" ); document.write( "\"-6x%2B2y=6\" obviously passes through (0,3),
\n" ); document.write( "because \"x=0\"-->\"2y=6\"-->\"y=3\" ,
\n" ); document.write( "and through (-1,0),
\n" ); document.write( "because \"y=0\"-->-6x=6}}}-->\"x=-1\"
\n" ); document.write( "Plotting points (0,3 and (-1,0), and connecting them with a straight line we get the graph for \"-6x%2B2y=6\" .
\n" ); document.write( "The graph for the system is
\n" ); document.write( " The lines are parallel, so there is no point (x,y) that belongs to both lines,meaning that there is no solution.
\n" ); document.write( "You can be sure that the lines are parallel because the have the same slope=3, as x increases by 1, y increases by 3.
\n" ); document.write( "Both lines make the same angle with the x-axis, and with all the gridlines parallel to the x-axis, as you can see from the red right triangles below:
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