document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181614>Question 181614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help understanding how to solve:\r<BR>\n" );
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document.write( "9x + 3y = 10.02<BR>\n" );
document.write( "6x + 4y =  8.26 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136225 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text {(1)          }\math 9x + 3y = 10.02\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text {(2)          }\math 6x + 4y =  8.26\">\r<BR>\n" );
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document.write( "Multiply (1) by 4:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text {(3)          }\math  36x + 12y = 40.08\">\r<BR>\n" );
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document.write( "Multiply (2) by -3:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text {(4)          }\math -18x - 12y = -24.78\">\r<BR>\n" );
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document.write( "Now that the coefficients on <i>y</i> are additive inverses, add (3) to (4):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text {(5)          }\math  18x + 0y = 15.3\">\r<BR>\n" );
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document.write( "Multiply by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac {1}{18}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text {(6)          }\math  x = \frac {15.3}{18} = 0.85\">\r<BR>\n" );
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document.write( "Substitute the value for <i>x</i> given in (6) into either (1) or (2) (I choose (1)):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text {                 }\math 9(0.85) + 3y = 10.02\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text {             \Rightarrow}\math 7.65 + 3y = 10.02\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text {             \Rightarrow}\math 3y = 2.37\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text {             \Rightarrow}\math y = 0.79\">\r<BR>\n" );
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document.write( "The solution set is the ordered pair (0.85, 0.79)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28%0D%0A400%2C+400%2C+-1%2C+2%2C+-1%2C+2%2C%0D%0Agrid%281%29%2C%0D%0Acircle%28.85%2C.79%2C.02%29%2C%0D%0Agraph%28%0D%0A400%2C+400%2C+-1%2C+2%2C+-1%2C+2%2C%0D%0Ay+=+-3x+%2B+3.34%2C%0D%0Ay+=+%28-3x%29%2F2+%2B+2.065%0D%0A%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Looks pretty close to me.\r<BR>\n" );
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document.write( "You could also have multiplied (1) by 2 and (2) by -3 (or by -2 and 3) so as to eliminate the <i>x</i> instead of the <i>y</i>, but ultimately the result would have been the same.  Verification is left as an exercise for the student.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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