document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204756>Question 204756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations, thank you<BR>\n" );
document.write( " 3x + 4y +  z =   7<BR>\n" );
document.write( "      2y +  z =   3<BR>\n" );
document.write( "-5x + 3y + 8z = -31 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154550 by </B><A HREF=/tutors/aboutme.mpl?userid=alicealc><B>alicealc(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=alicealc><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=154550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> eliminate x from the 1st and 3rd equations by:<BR>\n" );
document.write( "multiply the 1st equation by 5:<BR>\n" );
document.write( "15x + 20y + 5z = 35<BR>\n" );
document.write( "multiply the 3rd equation by 3:<BR>\n" );
document.write( "-15x + 9y + 24z = -93<BR>\n" );
document.write( "add them up:<BR>\n" );
document.write( "15x  + 20y + 5z  = 35<BR>\n" );
document.write( "-15x + 9y  + 24z = -93<BR>\n" );
document.write( "------------------------- (+)<BR>\n" );
document.write( "29y + 29z = -58<BR>\n" );
document.write( "------------------ (divide each side by 29)<BR>\n" );
document.write( "y + z = -2\r<BR>\n" );
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document.write( "subtract the 2nd equation from the problem with this new equation:<BR>\n" );
document.write( "2y + z = 3<BR>\n" );
document.write( "y  + z = -2<BR>\n" );
document.write( "------------- (-)<BR>\n" );
document.write( "y = 5\r<BR>\n" );
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document.write( "substitute the value of y into 2nd equation:<BR>\n" );
document.write( "2y + z = 3<BR>\n" );
document.write( "2*5 + z = 3<BR>\n" );
document.write( "10+ z = 3<BR>\n" );
document.write( "z = 3 - 10 = -7\r<BR>\n" );
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document.write( "substitute the value of y and z into the 1st equation:<BR>\n" );
document.write( "3x + 4y + z = 7<BR>\n" );
document.write( "3x + 4*5 + (-7) = 7<BR>\n" );
document.write( "3x + 20 - 7 = 7<BR>\n" );
document.write( "3x + 13 = 7<BR>\n" );
document.write( "3x = 7 - 13<BR>\n" );
document.write( "3x = -6<BR>\n" );
document.write( "x = -6/3 = -2\r<BR>\n" );
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document.write( "so, x = -2, y = 5, z = -7\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );