document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=498889>Question 498889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help solve this three linear equation containing three unknowns\r<BR>\n" );
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document.write( "x-3y+z=13<BR>\n" );
document.write( "3x+y-4z=13<BR>\n" );
document.write( "-4x-4y+2z=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #337231 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=337231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> please help solve this three linear equation containing three unknowns\r<BR>\n" );
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document.write( "x-3y+z=13<BR>\n" );
document.write( "3x+y-4z=13<BR>\n" );
document.write( "-4x-4y+2z=0<BR>\n" );
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document.write( "Solving for z in the 3rd equation gives:<BR>\n" );
document.write( "z = 2x + 2y<BR>\n" );
document.write( "Substitute this value into the other two equations:<BR>\n" );
document.write( "x - 3y + (2x + 2y) = 13 -> 3x - y = 13 [1]<BR>\n" );
document.write( "3x + y - 4(2x + 2y) = 13 -> -5x - 7y = 13 [2]<BR>\n" );
document.write( "Solve for y in [1], substitute into [2]:<BR>\n" );
document.write( "y = 3x - 13<BR>\n" );
document.write( "-5x - 7(3x - 13) = 13<BR>\n" );
document.write( "Simplify and solve for x:<BR>\n" );
document.write( "-5x - 21x + 91 = 13<BR>\n" );
document.write( "-26x = -78<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "From above, y = 3*3 - 13<BR>\n" );
document.write( "y = -4<BR>\n" );
document.write( "Therefore z = 2*3 + 2*-4<BR>\n" );
document.write( "z = -2 </SPAN>\n" );
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