document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4221>Question 4221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I asked a question on this set of equations a little while ago, but was wondering, could one use Cramers Rule to solve the following ..\r<BR>\n" );
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document.write( "a*4 + b*2 + c*9 + d * 7 = 21<BR>\n" );
document.write( "a* 2 + b*5 + c*4 + d*4 = 11.5<BR>\n" );
document.write( "a*6 + b*3 + c*5 + d*3 = 15.5<BR>\n" );
document.write( "a * 8 + b * 4 + c * 6 + d * 6 = 22\r<BR>\n" );
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document.write( "If so, I would be most grateful if someone could show me how ... or get me started anyway :)\r<BR>\n" );
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document.write( "And could a general 'formula' be created using this rule to solve other similar sets of equations? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1885 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> are your terms all powers? or is a*4 really 4a etc?\r<BR>\n" );
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document.write( "if they are coefficients then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%285%2C4%2C+4%2C2%2C9%2C7%2C21%2C+2%2C5%2C5%2C4%2C11.5%2C+6%2C3%2C5%2C3%2C15.5%2C+8%2C4%2C6%2C6%2C22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, the trouble is working out a 4x4 determinant. I do not have the time to walk though or type this here, so i advise you look on the web for a step-by-step guide to 4x4 matrices.\r<BR>\n" );
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document.write( "Anyway, Cramer's rule - ideal for this question.\r<BR>\n" );
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document.write( "work out the determinant, D for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C4%2C+4%2C2%2C9%2C7%2C+2%2C5%2C5%2C4%2C+6%2C3%2C5%2C3%2C+8%2C4%2C6%2C6%29 ALIGN=MIDDLE  ALT=\"matrix%284%2C4%2C+4%2C2%2C9%2C7%2C+2%2C5%2C5%2C4%2C+6%2C3%2C5%2C3%2C+8%2C4%2C6%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then work out the determinant, Da for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C4%2C+21%2C2%2C9%2C7%2C+11.5%2C5%2C5%2C4%2C+15.5%2C3%2C5%2C3%2C+22%2C4%2C6%2C6%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then do the same for Db, Dc and Dd -->\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C4%2C+4%2C21%2C9%2C7%2C+2%2C11.5%2C5%2C4%2C+6%2C15.5%2C5%2C3%2C+8%2C22%2C6%2C6%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C4%2C+4%2C2%2C21%2C7%2C+2%2C5%2C11.5%2C4%2C+6%2C3%2C15.5%2C3%2C+8%2C4%2C22%2C6%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C4%2C+4%2C2%2C9%2C21%2C+2%2C5%2C5%2C11.5%2C+6%2C3%2C5%2C15.5%2C+8%2C4%2C6%2C22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you are still sane, then:\r<BR>\n" );
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document.write( "a = Da/D\r<BR>\n" );
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document.write( "b = Db/D\r<BR>\n" );
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document.write( "c = Dc/D\r<BR>\n" );
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document.write( "d = Dd/D\r<BR>\n" );
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document.write( "jon </SPAN>\n" );
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