document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=137979>Question 137979</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395937787/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve this system?<BR>\n" );
document.write( "x + 2y-3z = -8<BR>\n" );
document.write( "2x + y + 3z= 17<BR>\n" );
document.write( "x - 3y + 3z = 11 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159330 by </B><A HREF=/tutors/aboutme.mpl?userid=AndrewRyan><B>AndrewRyan(3)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AndrewRyan><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=159330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Elimination by Addition or Subtraction<BR>\n" );
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document.write( "x + 2y-3z = -8  //First Equation<BR>\n" );
document.write( "2x + y + 3z= 17  //Second Equation<BR>\n" );
document.write( "x - 3y + 3z = 11  //Third Equation<BR>\n" );
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document.write( "Lets add the first and second equations to remove \"z\"<BR>\n" );
document.write( "    x + 2y - 3z = -8<BR>\n" );
document.write( "+  2x +  y + 3z =  17<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "   3x + 3y      =  9  //This will be our 4th equation<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Lets add the first and third equations to remove \"z\"<BR>\n" );
document.write( "    x + 2y - 3z = -8<BR>\n" );
document.write( "+   x - 3y + 3z =  11<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "   2x -  y      = 3 //This will be our 5th equation<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Reform the 4th equation<BR>\n" );
document.write( "3x + 3y =  9<BR>\n" );
document.write( "3x = 9 - 3y<BR>\n" );
document.write( "x = (9 - 3y)(1/3)<BR>\n" );
document.write( "x = 3 - y<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Now substitute this x value to the 5th equation<BR>\n" );
document.write( "2(3 - y) - y = 3<BR>\n" );
document.write( "6 - 2y - y = 3<BR>\n" );
document.write( "6 - 3y = 3<BR>\n" );
document.write( "-3y = 3 - 6<BR>\n" );
document.write( "-3y = -3<BR>\n" );
document.write( "y = 1 //Value for \"y\"<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Substitute this value of \"y\" to 4th equation<BR>\n" );
document.write( "3x + 3(1) =  9<BR>\n" );
document.write( "3x + 3 = 9<BR>\n" );
document.write( "3x = 9 - 3<BR>\n" );
document.write( "3x = 6<BR>\n" );
document.write( "x = 2<BR>\n" );
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document.write( "Now we have  the values for \"x\" and \"y\"<BR>\n" );
document.write( "Substitute this values of \"x\" and \"y\" to first equation<BR>\n" );
document.write( "(Actually you can substitute this to any of the first 3 equations)<BR>\n" );
document.write( "(2) + 2(1) - 3z = -8<BR>\n" );
document.write( "2 + 2 - 3z = -8<BR>\n" );
document.write( "4 - 3z = -8<BR>\n" );
document.write( "-3z = -8 - 4<BR>\n" );
document.write( "-3z = -12<BR>\n" );
document.write( "z = 4<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "To check your answer substitute and x-y-z values any of the first three equations (If you use the 1st equation to solve for z then you must not use it for checking. Same thing for the 2nd and the 3rd equations)<BR>\n" );
document.write( "I'll substitute to the 3rd equation<BR>\n" );
document.write( "(2) - 3(1) + 3(4) = 11<BR>\n" );
document.write( "2 - 3 + 12 = 11<BR>\n" );
document.write( "-1 + 12 = 11<BR>\n" );
document.write( "11 = 11 </SPAN>\n" );
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