document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175701>Question 175701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do I solve the system of equations 3r-4s+0 and 2r+5s=23? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130805 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=130805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are a few ways but lets use elimination method which means you want to manipulate the equation so the point where one set of terms are eliminated<BR>\n" );
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document.write( "I assumed that the +0 in eq 1 was really =0<BR>\n" );
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document.write( "3r-4s=0......eq 1  <BR>\n" );
document.write( "2r+5s=23.....eq 2<BR>\n" );
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document.write( "multiply all terms in eq 1 by 5 and all the terms in eq 2 by 4 and then add the 2 equations together. I will do the math then rewrite the equations next to one another so you can see what is taking place.<BR>\n" );
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document.write( "5(3r-4s=0)---->15r-20s=0  (revised eq 1)<BR>\n" );
document.write( "4(2r+5s=23)---->8r+20s=92 (revised eq 2)<BR>\n" );
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document.write( "can you see what happens to the s terms when we add the two equations together. They are eliminated because -20s+20s=0.  We are left with 15r+8r=92+0<BR>\n" );
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document.write( "23r=92<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=4%29 ALIGN=MIDDLE  ALT=\"highlight%28r=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "now take r's found value and plug it back into any equation. I am going to use eq 1<BR>\n" );
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document.write( "3(4)-4s=0--->12-4s=0--->4s=12<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28s=3%29 ALIGN=MIDDLE  ALT=\"highlight%28s=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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