document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=298024>Question 298024</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the system of equations<BR>\n" );
document.write( "3x+4y+z=7<BR>\n" );
document.write( "   2y+z=3<BR>\n" );
document.write( "-5x+3y+8z=-31<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 #214511 by </B><A HREF=/tutors/aboutme.mpl?userid=alex224><B>alex224(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=alex224><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=214511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x+4y+z=7<BR>\n" );
document.write( "   2y+z=3<BR>\n" );
document.write( "-5x+3y+8z=-31\r<BR>\n" );
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document.write( "the first step to solving this problem is to eliminate x form the 1st and last eqaution so you can solve for y or z\r<BR>\n" );
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document.write( "3x+4y+z=7<BR>\n" );
document.write( "-5x+3y+8z=-31\r<BR>\n" );
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document.write( "to eliminate x you need to multiply the first equation by 5 and the second equation by 3 and you get\r<BR>\n" );
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document.write( "15x+20y+5z=35<BR>\n" );
document.write( "-15x+9y+24z=-93\r<BR>\n" );
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document.write( "and the x's cancle out and you are left with\r<BR>\n" );
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document.write( "20y+5z=35<BR>\n" );
document.write( "9y+24z=-93\r<BR>\n" );
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document.write( "then you add the like terms in both of the ewuations and you should get\r<BR>\n" );
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document.write( "29y+29z=-58\r<BR>\n" );
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document.write( "once you have this equation you can use it with the 2nd equation from the origional equations \r<BR>\n" );
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document.write( "29y+29z=-58<BR>\n" );
document.write( "2y+z=3\r<BR>\n" );
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document.write( "then you need to choose a variable to solve for<BR>\n" );
document.write( "solve for y and to do so you need to sliminate z and multiply the second equation by -29\r<BR>\n" );
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document.write( "29y+29z=-58<BR>\n" );
document.write( "-58y-29z=-87\r<BR>\n" );
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document.write( "then you add the two equations together and z canles out\r<BR>\n" );
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document.write( "-29y=-148\r<BR>\n" );
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document.write( "devide both sides by -29\r<BR>\n" );
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document.write( "y=5\r<BR>\n" );
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document.write( "now that you know y you can plug it into one of above equations\r<BR>\n" );
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document.write( "3x+4y-7=7\r<BR>\n" );
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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=-6<BR>\n" );
document.write( "x=-2\r<BR>\n" );
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document.write( "now that you know both x and y you can plug them both into one of origional equations\r<BR>\n" );
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document.write( "2y+z=3\r<BR>\n" );
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document.write( "2(5)+z=3<BR>\n" );
document.write( "10+z=3<BR>\n" );
document.write( "z=-7\r<BR>\n" );
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document.write( "so the final answer is (-2,5,-7)\r<BR>\n" );
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