document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208209>Question 208209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SYSTEM OF 3 EQUATIONS WITH 3 UNKNOWNS<BR>\n" );
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document.write( "FIND SOLUTION SET FOR THE FOLLOWING SYSTEM OF EQUATIONS:\r<BR>\n" );
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document.write( " X  -Y  +5Z =  2<BR>\n" );
document.write( " 4X -3Y +5Z =  3<BR>\n" );
document.write( " 3X -2Y +4Z =  1<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157516 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=157516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
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( "                |  1  -1  5 |  2 |<BR>\n" );
document.write( "                |  4  -3  5 |  3 |<BR>\n" );
document.write( "                |  3  -2  4 |  1 |\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 =  |  1  -1   5 |  <BR>\n" );
document.write( "     |  4  -3   5 |  <BR>\n" );
document.write( "     |  3  -2   4 |  \r<BR>\n" );
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document.write( "D = 1(-12+10) - 4(-4+10) + 3(-5+15)<BR>\n" );
document.write( "D = 1(-2) -4(6) + 3(10)<BR>\n" );
document.write( "D = -2 -24 +30<BR>\n" );
document.write( "D = -26 +30\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+4 ALIGN=MIDDLE  ALT=\"D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Dx = |  2  -1   5 |  <BR>\n" );
document.write( "     |  3  -3   5 |  <BR>\n" );
document.write( "     |  1  -2   4 |\r<BR>\n" );
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document.write( "Dx = 2(-12+10) - 3(-4+10) +1(-5+15)<BR>\n" );
document.write( "Dx = 2(-2) - 3(6) + 1(10)<BR>\n" );
document.write( "Dx = -4 - 18 + 10<BR>\n" );
document.write( "Dx = -22 +10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Dx+=+-12 ALIGN=MIDDLE  ALT=\"Dx+=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Dy =  |  1   2   5 |  <BR>\n" );
document.write( "      |  4   3   5 |  <BR>\n" );
document.write( "      |  3   1   4 | \r<BR>\n" );
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document.write( "Dy = 1(12-5) -4(8-5) +3(10-15)<BR>\n" );
document.write( "Dy = 1(7) -4(3) +3(-5)<BR>\n" );
document.write( "Dy = 7 -12 -15<BR>\n" );
document.write( "Dy = -5 -15\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Dy+=+-20 ALIGN=MIDDLE  ALT=\"Dy+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Dz = |  1  -1   2 |  <BR>\n" );
document.write( "     |  4  -3   3 |  <BR>\n" );
document.write( "     |  3  -2   1 |\r<BR>\n" );
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document.write( "Dz = 1(-3+6)- 4(-1+4)+ 3(-3+6)<BR>\n" );
document.write( "Dz = 1(3) - 4(3) + 3(3)<BR>\n" );
document.write( "Dz = 3 -12 + 9<BR>\n" );
document.write( "Dz = -9 + 9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Dz+=+0 ALIGN=MIDDLE  ALT=\"Dz+=+0\"   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=x+=+Dx%2FD+=+-12%2F4 ALIGN=MIDDLE  ALT=\"x+=+Dx%2FD+=+-12%2F4\"   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+=+-20%2F4 ALIGN=MIDDLE  ALT=\"y+=+Dy%2FD+=+-20%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-5 ALIGN=MIDDLE  ALT=\"y+=+-5\"   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+=+0%2F4 ALIGN=MIDDLE  ALT=\"z+=+Dz%2FD+=+0%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+0 ALIGN=MIDDLE  ALT=\"z+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer: The solution set is {(-3,-5, 0)}\r<BR>\n" );
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