document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104946>Question 1104946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by back substitution.<BR>\n" );
document.write( "2x+4y+z+3w=1<BR>\n" );
document.write( "-2y-12z-4w=-16<BR>\n" );
document.write( "z+w=2<BR>\n" );
document.write( "-5w=-15<BR>\n" );
document.write( "The solution set is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719674 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=719674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "Start from the bottom equation and work your way up<BR>\n" );
document.write( "Solve the fourth equation for w<BR>\n" );
document.write( "-5w=-15<BR>\n" );
document.write( "-5w/(-5)=-15/(-5)<BR>\n" );
document.write( "w = 3\r<BR>\n" );
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document.write( "Then use that value of w to plug into the third equation. Notice we're going backwards or up the chain of equations. After w is replaced, solve for z<BR>\n" );
document.write( "z+w = 2<BR>\n" );
document.write( "z+3 = 2<BR>\n" );
document.write( "z+3-3 = 2-3<BR>\n" );
document.write( "z = -1\r<BR>\n" );
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document.write( "Now use z = -1 and w = 3 to plug into the second equation. Solve for y<BR>\n" );
document.write( "-2y-12z-4w = -16<BR>\n" );
document.write( "-2y-12(-1)-4(3) = -16<BR>\n" );
document.write( "-2y+12-12 = -16<BR>\n" );
document.write( "-2y = -16<BR>\n" );
document.write( "-2y/(-2) = -16/(-2)<BR>\n" );
document.write( "y = 8\r<BR>\n" );
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document.write( "Use y = 8, z = -1, w = 3 to plug into the first equation. Solve for x<BR>\n" );
document.write( "2x+4y+z+3w=1<BR>\n" );
document.write( "2x+4(8)+(-1)+3(3)=1<BR>\n" );
document.write( "2x+32-1+9=1<BR>\n" );
document.write( "2x+40=1<BR>\n" );
document.write( "2x+40-40=1-40<BR>\n" );
document.write( "2x=-39<BR>\n" );
document.write( "2x/2=-39/2<BR>\n" );
document.write( "x = -39/2\r<BR>\n" );
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document.write( "The value of x as a fraction is x = -39/2<BR>\n" );
document.write( "The value of x in decimal form is x = -19.5\r<BR>\n" );
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document.write( "In summary we got the following values<BR>\n" );
document.write( "x = -39/2<BR>\n" );
document.write( "y = 8<BR>\n" );
document.write( "z = -1<BR>\n" );
document.write( "w = 3\r<BR>\n" );
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document.write( "So the solution is (x,y,z,w) = <font color=red>(-39/2, 8, -1, 3)</font>\r<BR>\n" );
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document.write( "Note: you can optionally express -39/2 as -19.5<BR>\n" );
document.write( "If you do so, then the solution would be (x,y,z,w) = <font color=red>(-19.5, 8, -1, 3)</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
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