document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102281>Question 102281</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please take the time to help me solve this problem: Solve the following system of three linear equations: x – 2y = 4 and 2 x – 3 y + 2 z = <BR>\n" );
document.write( "– 2 and 4 x – 7 y + 2 z = 6. Noting that each equation represents a plane, interpret your result.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you, for taking the time to help me </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74355 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=74355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  x  – 2y    0z  =  4  <BR>\n" );
document.write( "2 x – 3 y + 2 z = – 2 <BR>\n" );
document.write( "4 x – 7 y + 2 z = 6<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "x = 2y+4<BR>\n" );
document.write( "Substitute to get:<BR>\n" );
document.write( "2(2y+4)-3y+2z = -1<BR>\n" );
document.write( "4(2y+4)-7y+2z = 6<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Simplify:<BR>\n" );
document.write( "x = 2y+4<BR>\n" );
document.write( "y + 2z = 9<BR>\n" );
document.write( "y + 2z = -2<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The last two equations indicate the system is inconsistent.<BR>\n" );
document.write( "Two of the equations represent parallel planes.<BR>\n" );
document.write( "There is no intersection of the three planes represented<BR>\n" );
document.write( "by the original three equations.<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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