document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117615>Question 117615</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0201356651/algebrahomeworkh>basic technical mathematics with calculus</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve the linear equations:\r<BR>\n" );
document.write( "\n" );
document.write( "A + B + C = 0<BR>\n" );
document.write( "4A - 10B = 3<BR>\n" );
document.write( "-10B + 5C = 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85609 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+B+%2B+C+=+0 ALIGN=MIDDLE  ALT=\"A+%2B+B+%2B+C+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A+-+10B+=+3 ALIGN=MIDDLE  ALT=\"4A+-+10B+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10B+%2B+5C+=+6 ALIGN=MIDDLE  ALT=\"-10B+%2B+5C+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The quickest and easiest way is to use equations 2 and 3 and find expressions for A and C in terms of B and then substitute those into equation 1. <BR>\n" );
document.write( "You then solve for B and go back and solve for A and C.<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A+-+10B+=+3 ALIGN=MIDDLE  ALT=\"4A+-+10B+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A=3%2B10B ALIGN=MIDDLE  ALT=\"4A=3%2B10B\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%283%2B10B%29%2F4 ALIGN=MIDDLE  ALT=\"A=%283%2B10B%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10B+%2B+5C+=+6 ALIGN=MIDDLE  ALT=\"-10B+%2B+5C+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5C=6%2B10B ALIGN=MIDDLE  ALT=\"5C=6%2B10B\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=%286%2B10B%29%2F5 ALIGN=MIDDLE  ALT=\"C=%286%2B10B%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now go back to equation 1.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+B+%2B+C+=+0 ALIGN=MIDDLE  ALT=\"A+%2B+B+%2B+C+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B10B%29%2F4+%2B+B+%2B%286%2B10B%29%2F5+=+0 ALIGN=MIDDLE  ALT=\"%283%2B10B%29%2F4+%2B+B+%2B%286%2B10B%29%2F5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's multiply both sides by (4*5) to get rid of the denominators.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B10B%29%2F4+%2B+B+%2B%286%2B10B%29%2F5+=+0 ALIGN=MIDDLE  ALT=\"%283%2B10B%29%2F4+%2B+B+%2B%286%2B10B%29%2F5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%283%2B10B%29%2B20B%2B4%286%2B10B%29=0 ALIGN=MIDDLE  ALT=\"5%283%2B10B%29%2B20B%2B4%286%2B10B%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2B50B%2B20B%2B24%2B40B=0 ALIGN=MIDDLE  ALT=\"15%2B50B%2B20B%2B24%2B40B=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110B%2B39=0 ALIGN=MIDDLE  ALT=\"110B%2B39=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110B=-39 ALIGN=MIDDLE  ALT=\"110B=-39\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B=-39%2F110%29 ALIGN=MIDDLE  ALT=\"highlight%28B=-39%2F110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From our derivation above for A,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%283%2B10B%29%2F4 ALIGN=MIDDLE  ALT=\"A=%283%2B10B%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A=3%2B10%28-39%2F110%29 ALIGN=MIDDLE  ALT=\"4A=3%2B10%28-39%2F110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A=330%2F110-390%2F110%29 ALIGN=MIDDLE  ALT=\"4A=330%2F110-390%2F110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A=-60%2F110%29 ALIGN=MIDDLE  ALT=\"4A=-60%2F110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-15%2F110%29 ALIGN=MIDDLE  ALT=\"A=-15%2F110%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=-3%2F22%29%29 ALIGN=MIDDLE  ALT=\"highlight%28A=-3%2F22%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From equation 1, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC=0 ALIGN=MIDDLE  ALT=\"A%2BB%2BC=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15%2F110-39%2F110%2BC=0 ALIGN=MIDDLE  ALT=\"-15%2F110-39%2F110%2BC=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=%2839%2B15%29%2F110 ALIGN=MIDDLE  ALT=\"C=%2839%2B15%29%2F110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=54%2F110 ALIGN=MIDDLE  ALT=\"C=54%2F110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=27%2F55%29 ALIGN=MIDDLE  ALT=\"highlight%28C=27%2F55%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );