document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314092>Question 314092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "I have to solve a linear equation but can not find a solution.<BR>\n" );
document.write( "Please help me how to calculate.\r<BR>\n" );
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document.write( "x+y+z+u=1<BR>\n" );
document.write( "2x+3y-4z+5u=2<BR>\n" );
document.write( "3x+4y-3z+6u=0\r<BR>\n" );
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document.write( "Thank you sooo much in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224528 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=224528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It appears there is no solution to this system of equations.\r<BR>\n" );
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document.write( "The fact becomes clear when you try to eliminate variables and wind up with an equation such as 0 = something that is not equal to 0.\r<BR>\n" );
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document.write( "Since this equation is not true, the system of equations has no solution.\r<BR>\n" );
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document.write( "If you had come up with a row that says something like 0 = 0 which is true, then the system of equations would probably have had a dependent solution which means that the solution depends on the value of one of the variables.\r<BR>\n" );
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document.write( "Since  you started with a system of 3 equations in 4 unknowns, the best you could have hoped for would have been a dependent solution.\r<BR>\n" );
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document.write( "I will go through the solution to show you what happened.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Your equations are:\r\n" );
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document.write( "               1x   +   1y   +   1z   +   1u   =   1\r\n" );
document.write( "               2x   +   3y   -   4z   +   5u   =   2\r\n" );
document.write( "               3x   +   4y   -   3z   +   6u   =   0\r\n" );
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document.write( "Subtract 2 times row 1 from row 2 to get:\r\n" );
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document.write( "               0x   +   1y   -   6z   +   3u   =    0\r\n" );
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document.write( "Subtract 3 times row 1 from row 3 to get:\r\n" );
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document.write( "               0x   +   1y   -   6z   +   3u   =   -3\r\n" );
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document.write( "You are left with 2 equations in 3 unknowns.\r\n" );
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document.write( "They are:\r\n" );
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document.write( "               1y   -   6z   +   3u   =    0\r\n" );
document.write( "               1y   -   6z   +   3u   =   -3\r\n" );
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document.write( "If you subtract the first equation from the second equation you will get:\r\n" );
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document.write( "                                  0   =   -3\r\n" );
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document.write( "Since 0 = -3 is false, this leads to the conclusion that there is no solution to this system of equations.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "In order for there to be a unique solution to this system of equations, you would have had to have 4 equations in 4 unknowns.\r<BR>\n" );
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document.write( "           \r<BR>\n" );
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document.write( " </SPAN>\n" );
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