document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1799>Question 1799</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the system<BR>\n" );
document.write( "x+y+z=6<BR>\n" );
document.write( "3x+4y-7z=1<BR>\n" );
document.write( "2x-y+3z=5<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #613 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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/cgi-bin/show-face.mpl?user=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> these are just simultaneous equations...3 unknowns and 3 equations...solvable, if tedious.\r<BR>\n" );
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document.write( "You need to start with 2 equations and get rid of 1 variable...looking at the 3 equations, use 1 and 3, as they both have a y, so easy to remove these...\r<BR>\n" );
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document.write( "1 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+y+%2B++z+=+6 ALIGN=MIDDLE  ALT=\"+x+%2B+y+%2B++z+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+y+%2B+3z+=+5 ALIGN=MIDDLE  ALT=\"2x+-+y+%2B+3z+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the y's have Different signs so aDD (note the DD). Similarly, Same signs, then Subtract!!\r<BR>\n" );
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document.write( "so, we get equation 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+4z+=+11 ALIGN=MIDDLE  ALT=\"3x+%2B+4z+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now repeat the process with 2 other equations, say 2 and 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+4y+-+7z+=+1 ALIGN=MIDDLE  ALT=\"3x+%2B+4y+-+7z+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-++y+%2B+3z+=+5 ALIGN=MIDDLE  ALT=\"2x+-++y+%2B+3z+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Again I will choose to get rid of the y term, but i need to increase the lower equation by a factor of 4, to get the 2 equations to match....\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+4y+-++7z+=++1 ALIGN=MIDDLE  ALT=\"3x+%2B+4y+-++7z+=++1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+-+4y+%2B+12z+=+20 ALIGN=MIDDLE  ALT=\"8x+-+4y+%2B+12z+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The y-terms have Different signs therefore we aDD, getting equation 5...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x+%2B+5z+=+21 ALIGN=MIDDLE  ALT=\"11x+%2B+5z+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we use 4 and 5 to get rid of another variable...i choose to remove the z's, by making them both 20z...\r<BR>\n" );
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document.write( "equation 4 needs to be multiplied by 5: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+4z+=+11 ALIGN=MIDDLE  ALT=\"+3x+%2B+4z+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "equation 5 needs to be multiplied by 4: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x+%2B+5z+=+21 ALIGN=MIDDLE  ALT=\"11x+%2B+5z+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "This gives us\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x+%2B+20z+=+55 ALIGN=MIDDLE  ALT=\"15x+%2B+20z+=+55\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44x+%2B+20z+=+84 ALIGN=MIDDLE  ALT=\"44x+%2B+20z+=+84\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here the z terms have the Same sign therefore we Subtract the 2 equations, giving us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-29x%29=%28-29%29 ALIGN=MIDDLE  ALT=\"%28-29x%29=%28-29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so x=1.\r<BR>\n" );
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document.write( "We now substitute this into 4 or 5, to find z (z=2) and then these into equation 1, 2 or 3 to find y (y=3).\r<BR>\n" );
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document.write( "THEN you double check each of the original equations (1, 2 and 3) to make sure that your answers are correct.\r<BR>\n" );
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document.write( "cheers<BR>\n" );
document.write( "Jon. </SPAN>\n" );
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