document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133058>Question 133058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having problems with the following system of equations.  The elimination method is supposed to be used, and the solution is to be in the form of integers or fractions.\r<BR>\n" );
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document.write( ".03x-0.2y=4<BR>\n" );
document.write( ".04x+0.5y=63/19\r<BR>\n" );
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document.write( "Thanks!\r<BR>\n" );
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document.write( "Stephanie </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97283 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=97283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume you are being asked to eliminate rather than use substitution.\r<BR>\n" );
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document.write( "Given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.03x-0.2y=4 ALIGN=MIDDLE  ALT=\".03x-0.2y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >    Equation A<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.04x%2B0.5y=63%2F19 ALIGN=MIDDLE  ALT=\".04x%2B0.5y=63%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Equation B\r<BR>\n" );
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document.write( "In order to use elimination, you want to get the coefficients of one of the variables (let's say y in this case) to be the same. Then you can simply add/substract one equation from the other to eliminate that variable. Once you have a single variable left, you can solve for it easily enough.\r<BR>\n" );
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document.write( "So let's manipulate equation A above. Let's multiply it by 5. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.15x+-+y+=+20 ALIGN=MIDDLE  ALT=\"+0.15x+-+y+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now manipulate equation B. Let's multiply it by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.8x+%2B+y+=+126%2F19 ALIGN=MIDDLE  ALT=\"+0.8x+%2B+y+=+126%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then add these two equesitons to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.23x+=+20%2B+126%2F19+ ALIGN=MIDDLE  ALT=\"+0.23x+=+20%2B+126%2F19+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solve for x, then use that to solve for y in any of the equations above.\r<BR>\n" );
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document.write( "So now the question?? How did we know to use 5 and 2? Great question. We need to find a way to make the coefficients of one of the variables end up being equal in order to add/subtract them. You can look at Equation A and see that if you multiply by 5 it becomes 1. Then pick a number to multiply equation B to also se the y coefficient to 1 (in this case that number is 2). </SPAN>\n" );
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