document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72620>Question 72620</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131492594/algebrahomeworkh>Introductory and intermediate algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> solve this system of equations.  if it is unsolvable say so.<BR>\n" );
document.write( "3x + 4y + 5z=8<BR>\n" );
document.write( "1x - 2y + 3z= -6<BR>\n" );
document.write( "2x - 4y + 6z=8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52018 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Unsolvable.<BR>\n" );
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document.write( "In order to be a solvable system for three variables, all three equations must be independent.<BR>\n" );
document.write( "But look at the left sides of equations two and three. If you multiply both sides of the<BR>\n" );
document.write( "second equation by 2 you get:<BR>\n" );
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document.write( "2x - 4y + 6z = -12<BR>\n" );
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document.write( "Notice that the left side of this equation is identical to the left side of equation 3.<BR>\n" );
document.write( "That indicates that the graph of the line represented by equation two is parallel to the<BR>\n" );
document.write( "graph of the line represented by equation 3.  Since they are parallel lines they never <BR>\n" );
document.write( "intersect at a common point, so they can't have a common solution.  <BR>\n" );
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document.write( "If you are familiar with Cramer's rule you can calculate the determinant of the coefficients<BR>\n" );
document.write( "on the left side of these 3 equations, and the determinant equals zero.  This also<BR>\n" );
document.write( "indicates that there is no common solution for these three equations.<BR>\n" );
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document.write( "Hope this explanation helps you to understand why you can say the equations have no common<BR>\n" );
document.write( "solution just by inspecting them.<BR>\n" );
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