document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182662>Question 182662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1/5x+y=6/5<BR>\n" );
document.write( "1/10x+1/3y=5/6\r<BR>\n" );
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document.write( "Using elimination, not substitution.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137145 by </B><A HREF=/tutors/aboutme.mpl?userid=MathGuyJoe><B>MathGuyJoe(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathGuyJoe><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=137145\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F5%29x+%2B+y+=+6%2F5+ ALIGN=MIDDLE  ALT=\"+%281%2F5%29x+%2B+y+=+6%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F10%29x+%2B+%281%2F3%29y+=+5%2F6+ ALIGN=MIDDLE  ALT=\"+%281%2F10%29x+%2B+%281%2F3%29y+=+5%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By rule, you can multiply both sides of an equation by any constant without changing the result, so let's do this to both equations to get rid of the fractions.  We'll multiply each element in the top equation by 5 and we'll multiply each element in the bottom equation by 30 (the least common multiple).  That leaves us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+5y+=+6+ ALIGN=MIDDLE  ALT=\"+x+%2B+5y+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+10y+=+25+ ALIGN=MIDDLE  ALT=\"+3x+%2B+10y+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now that we don't have any fractions, let's get to work.  In order to eliminate a variable, we need to choose a multiplier for one of the equations that, when added to the other equation, will cancel out either the x or the y.  Let's cancel out the y's by multiplying the top equation by -2.  That gives us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2x+-+10y+=+-12+ ALIGN=MIDDLE  ALT=\"+-2x+-+10y+=+-12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now adding that to our second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+10y+=+25+ ALIGN=MIDDLE  ALT=\"+3x+%2B+10y+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Gives us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2x+%2B+3x%29+%2B+%28-10y+%2B+10y%29+=+-12+%2B+25+ ALIGN=MIDDLE  ALT=\"+%28-2x+%2B+3x%29+%2B+%28-10y+%2B+10y%29+=+-12+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+13+ ALIGN=MIDDLE  ALT=\"+x+=+13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Plugging 13 back into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+5y+=+6+ ALIGN=MIDDLE  ALT=\"+x+%2B+5y+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in place of x gives us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2813%29+%2B+5y+=+6+ ALIGN=MIDDLE  ALT=\"+%2813%29+%2B+5y+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5y+=+-7+ ALIGN=MIDDLE  ALT=\"+5y+=+-7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-7%2F5+ ALIGN=MIDDLE  ALT=\"+y+=+-7%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So our final answers are <b>x = 13</b> and <b>y = -7/5</b>.<BR>\n" );
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document.write( "For confirmation, take these x and y values and plug them back into each of the original equations -- after a bunch of fraction work, you'll find the answers check out.  =)<BR>\n" );
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document.write( "Hope this helps.  ~ Joe </SPAN>\n" );
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