document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183002>Question 183002</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495117943/algebrahomeworkh>Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I need help Please with the following problem. <BR>\n" );
document.write( "Solve the system:<BR>\n" );
document.write( "2x + y + Z + w = 3<BR>\n" );
document.write( "x - 2y - z + w = -3<BR>\n" );
document.write( "x - y - 2z - w = -3<BR>\n" );
document.write( "x + y - z + 2w = 4\r<BR>\n" );
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document.write( "I have tried adding 1 & 2 getting 3x - y + 2w = 0<BR>\n" );
document.write( "Then taking 1 & multiplying it by 2 and then adding it to 3 and getting 5x+y=w=3<BR>\n" );
document.write( "Then taking 4 & mutliplying it by -2 then adding it to 1 getting 3x+2y+3w=1\r<BR>\n" );
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document.write( "Then I am stuck because I don't know what to do next.  I know I have to get rid of the same 2 variables.  Any help would be greatly appreciated.\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Jen<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 #137375 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=137375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x + y + Z + w = 3<BR>\n" );
document.write( "x - 2y - z + w = -3<BR>\n" );
document.write( "x - y - 2z - w = -3<BR>\n" );
document.write( "x + y - z + 2w = 4 <BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Interchange 1st and 2nd to get:<BR>\n" );
document.write( "x - 2y - z + w = -3<BR>\n" );
document.write( "2x + y + Z + w = 3<BR>\n" );
document.write( "x - y - 2z - w = -3<BR>\n" );
document.write( "x + y - z + 2w = 4 <BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Subtract two times the 1st equation from the 2nd; subtract the 1st equation <BR>\n" );
document.write( "from the 3rd; subtract the 1st equation from the 4th equation to get:<BR>\n" );
document.write( "x - 2y - z + w = -3<BR>\n" );
document.write( "0 + 5y + 3Z - w = 9<BR>\n" );
document.write( "0 + y -  z - 2w = 0<BR>\n" );
document.write( "0 + 3y + 0 +  w = 7 <BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Interchange the 2nd equation and the 3rd equation to get:<BR>\n" );
document.write( "x - 2y - z + w = -3<BR>\n" );
document.write( "0 + y -  z - 2w = 0<BR>\n" );
document.write( "0 + 5y + 3Z - w = 9<BR>\n" );
document.write( "0 + 3y + 0 +  w = 7 <BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Subtract 5 times the 2nd equation from the 3rd ; subtract 3 times the 2nd equation from the 4th to get:\r<BR>\n" );
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document.write( "x - 2y - z + w = -3<BR>\n" );
document.write( "0 + y -  z - 2w = 0<BR>\n" );
document.write( "0 + 0 + 8Z + 9w = 9<BR>\n" );
document.write( "0 + 0 + +3z + 7w = 7 <BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Solve 3rd and 4th as a systme:<BR>\n" );
document.write( "8Z + 9w = 9<BR>\n" );
document.write( "3z + 7w = 7<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Multiply 1st equation by 3 and the 2nd equation by 8 to get:<BR>\n" );
document.write( "24z + 27w = 27<BR>\n" );
document.write( "24z + 56w = 56<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Subtract the 1st equation from the 2nd equation to get:<BR>\n" );
document.write( "29w = 29<BR>\n" );
document.write( "w = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Substitute to solve for \"z\":<BR>\n" );
document.write( "3z + 56 = 56<BR>\n" );
document.write( "z = 0<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Substitute those values in the following equations to solve for x and for y.<BR>\n" );
document.write( "x - 2y - z + w = -3<BR>\n" );
document.write( "0 + y -  z - 2w = 0<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "x -2y - 0 + 1 = -3<BR>\n" );
document.write( "0 + y - 0 - 2 = 0<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "x-2y = -4<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Therefore x - 2*2 = -4<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Ans: x = 0 ; y = 2 ; z = 0 ; w = 1<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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