document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208208>Question 208208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SYSTEM OF 3 EQUATIONS WITH 3 UNKNOWNS\r<BR>\n" );
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document.write( "FIND THE SOLUTION SET FOR THE FOLLOWING SYSTEM OF EQUATIONS:\r<BR>\n" );
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document.write( " 4X -2Y -3Z =  8<BR>\n" );
document.write( " 5X +3Y -4Z =  4<BR>\n" );
document.write( " 6X -4Y -5Z = 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157517 by </B><A HREF=/tutors/aboutme.mpl?userid=pjalgeb><B>pjalgeb(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=pjalgeb><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=157517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> REQUIRED: Find the solution set {(x, y z)} for the system given.\r<BR>\n" );
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document.write( "SOLUTION:\r<BR>\n" );
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document.write( "The augmented 3x3 matrix for the above system of equations is:\r<BR>\n" );
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document.write( "                |  4  -2  -3 |  8 |<BR>\n" );
document.write( "                |  5   3  -4 |  4 |<BR>\n" );
document.write( "                |  6  -4  -5 | 12 |\r<BR>\n" );
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document.write( "By Cramers Rule:  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+Dx%2FD ALIGN=MIDDLE  ALT=\"x+=+Dx%2FD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+Dy%2FD ALIGN=MIDDLE  ALT=\"y+=+Dy%2FD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+Dz%2FD ALIGN=MIDDLE  ALT=\"z+=+Dz%2FD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First, lets solve for D, Dx, Dy and Dz:\r<BR>\n" );
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document.write( "D =  |  4  -2  -3 | <BR>\n" );
document.write( "     |  5   3  -4 | <BR>\n" );
document.write( "     |  6  -4  -5 | \r<BR>\n" );
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document.write( "D = 4(-15-16) -5(10-12) +6(8+9)<BR>\n" );
document.write( "D = 4(-31) -5(-2)+ 6(17)<BR>\n" );
document.write( "D = -124 +10 +102<BR>\n" );
document.write( "D = -124 -112\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+-12 ALIGN=MIDDLE  ALT=\"D+=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Dx = |  8  -2  -3 | <BR>\n" );
document.write( "     |  4   3  -4 | <BR>\n" );
document.write( "     | 12  -4  -5 |\r<BR>\n" );
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document.write( "Dx = 8(-15-16) -4(10-12) + 12(8+9)<BR>\n" );
document.write( "Dx = 8(-31) -4(-2) + 12(17)<BR>\n" );
document.write( "Dx = -248 +8 + 204<BR>\n" );
document.write( "Dx = -248 +212\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Dx+=+-36 ALIGN=MIDDLE  ALT=\"Dx+=+-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Dy = |  4   8  -3 | <BR>\n" );
document.write( "     |  5   4  -4 | <BR>\n" );
document.write( "     |  6  12  -5 | \r<BR>\n" );
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document.write( "Dy = 4(-20+48) -5(-40+36) +6(-32+12)<BR>\n" );
document.write( "Dy = 4(28) -5(-4) +6(-20)<BR>\n" );
document.write( "Dy = 112 +20 -120<BR>\n" );
document.write( "Dy = 132 -120\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Dy+=+12 ALIGN=MIDDLE  ALT=\"Dy+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Dz = |  4  -2   8 | <BR>\n" );
document.write( "     |  5   3   4 |  <BR>\n" );
document.write( "     |  6  -4  12 |\r<BR>\n" );
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document.write( "Dz = 4(36+16) -5(-24+32) +6(-8-24)<BR>\n" );
document.write( "Dz = 4(52) -5(8) +6(-32)<BR>\n" );
document.write( "Dz = 208 -40 -192<BR>\n" );
document.write( "Dz = 168 -192\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+Dx%2FD+=+-36%2F-12 ALIGN=MIDDLE  ALT=\"x+=+Dx%2FD+=+-36%2F-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+Dy%2FD+=+12%2F-12 ALIGN=MIDDLE  ALT=\"y+=+Dy%2FD+=+12%2F-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-1 ALIGN=MIDDLE  ALT=\"y+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+Dz%2FD+=+-24%2F-12 ALIGN=MIDDLE  ALT=\"z+=+Dz%2FD+=+-24%2F-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+2 ALIGN=MIDDLE  ALT=\"z+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer: The solution set is {(3,-1,2)} </SPAN>\n" );
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