document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346673>Question 346673</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Algebra- solving sytems of equations in three varaiables: \r<BR>\n" );
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document.write( "( Answer is needed within 1.5 hours, by 11\"30 AM Pacific time - Thanks!)\r<BR>\n" );
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document.write( "3x+5y+4z =13<BR>\n" );
document.write( "5z+2y+3z=-9<BR>\n" );
document.write( "6x+3y+4z=-8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247883 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=247883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Algebra- solving sytems of equations in three varaiables: <BR>\n" );
document.write( "( Answer is needed within 1.5 hours, by 11\"30 AM Pacific time - Thanks!) <BR>\n" );
document.write( "3x+5y+4z =13<BR>\n" );
document.write( "5z+2y+3z=-9  (--> assuming this is 5x + 2y + 3z = -9)<BR>\n" );
document.write( "6x+3y+4z=-8\r<BR>\n" );
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document.write( "using method of elimination, choosing z first since I see two 4z's\r<BR>\n" );
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document.write( "use 1st equation and multiply 3rd equation by -1\r<BR>\n" );
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document.write( " 3x + 5y + 4z = 13<BR>\n" );
document.write( "-6x - 3y - 4z =  8<BR>\n" );
document.write( "add these to get -3x + 2y = 21\r<BR>\n" );
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document.write( "use 1st equation multiplied by 3 and 2nd equation multipled by -4\r<BR>\n" );
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document.write( "  9x + 15y + 12z = 39<BR>\n" );
document.write( "-20x -  8y - 12z = 36<BR>\n" );
document.write( "add these to get -11x + 7y = 75\r<BR>\n" );
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document.write( "we now have:<BR>\n" );
document.write( " -3x + 2y = 21 (multiply this one by 7)<BR>\n" );
document.write( "-11x + 7y = 75 (multiply this one by -2)\r<BR>\n" );
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document.write( "to get:<BR>\n" );
document.write( "-21x + 14y =  147<BR>\n" );
document.write( " 22x - 14y = -150<BR>\n" );
document.write( "add these to get x = -3\r<BR>\n" );
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document.write( "plug x = -3 into -3x + 2y = 21<BR>\n" );
document.write( "-3(-3) + 2y = 21<BR>\n" );
document.write( "9 + 2y = 21<BR>\n" );
document.write( "2y = 12<BR>\n" );
document.write( "y = 6\r<BR>\n" );
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document.write( "now going back to the original equations, plug x = -3 and y = 6<BR>\n" );
document.write( "into 3x + 5y + 4z = 13<BR>\n" );
document.write( "3(-3) + 5(6) + 4z = 13<BR>\n" );
document.write( "-9 + 30 + 4z = 13<BR>\n" );
document.write( "21 + 4z = 13<BR>\n" );
document.write( "4z = -8<BR>\n" );
document.write( "z = -2\r<BR>\n" );
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document.write( "solution is (-3,6,-2)\r<BR>\n" );
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document.write( "hope this helps you\r<BR>\n" );
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document.write( " </SPAN>\n" );
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