document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=207711>Question 207711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for X, Y, and Z in the following systems of three equations using either substition or elimination methods:<BR>\n" );
document.write( "a. X + 2Y + Z = 6<BR>\n" );
document.write( "    X + Y  = 4<BR>\n" );
document.write( "    3X + Y + Z =  8\r<BR>\n" );
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document.write( "b. 10X + Y + Z = 12<BR>\n" );
document.write( "    8X + 2Y +Z  = 11<BR>\n" );
document.write( "    20X - 10Y - 2Z = 8\r<BR>\n" );
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document.write( "c. 22X + 5Y + 7Z = 12<BR>\n" );
document.write( "    10X + 3Y + 2Z = 5<BR>\n" );
document.write( "    9X  +  2Y +  12Z = 14<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157383 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=157383\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "PROBLEM A\r<BR>\n" );
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document.write( "GIVEN: <BR>\n" );
document.write( " X + 2Y + Z = 6  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "      X + Y = 4  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 3X + Y + Z = 8  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "REQUIRED: FIND X, Y AND Z\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "SOLUTION:<BR>\n" );
document.write( "FROM <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "X + Y = 4<BR>\n" );
document.write( "    Y = 4-X --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+4 ALIGN=MIDDLE  ALT=\"Equation+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "MULTIPLY <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > WITH -1 AND ADD TO <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > TO ELIMINATE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "    -X -2Y - Z = -6  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "ADD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "    -X -2Y - Z = -6  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    3X + Y + Z =  8  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    _______________<BR>\n" );
document.write( "    2X -Y      =  2 \r<BR>\n" );
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document.write( "         2X -Y = 2   --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+6 ALIGN=MIDDLE  ALT=\"Equation+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOW WE CAN SOLVE FOR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > USING <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+4 ALIGN=MIDDLE  ALT=\"Equation+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+6 ALIGN=MIDDLE  ALT=\"Equation+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > BY SUBSTITUTION:\r<BR>\n" );
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document.write( "         2X -Y = 2  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+6 ALIGN=MIDDLE  ALT=\"Equation+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "     2X -(4-X) = 2<BR>\n" );
document.write( "     2X -4 + X = 2<BR>\n" );
document.write( "            3X = 2 + 4<BR>\n" );
document.write( "            3X = 6<BR>\n" );
document.write( "             X = 6/3<BR>\n" );
document.write( "             <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+2 ALIGN=MIDDLE  ALT=\"X+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "NOW THAT WE HAVE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" >, WE CAN SOLVE FOR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" > USING <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=2 ALIGN=MIDDLE  ALT=\"X=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > BY SUBSTITUTION: \r<BR>\n" );
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document.write( "         X + Y = 4  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "         2 + Y = 4<BR>\n" );
document.write( "             Y = 4-2<BR>\n" );
document.write( "             <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+2 ALIGN=MIDDLE  ALT=\"Y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "NOW THAT WE HAVE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, WE CAN SOLVE FOR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" > USING <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > BY SUBSTITUTION:\r<BR>\n" );
document.write( "\n" );
document.write( "    X + 2Y + Z = 6  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  2 + 2(2) + Z = 6  <BR>\n" );
document.write( "     2 + 4 + Z = 6<BR>\n" );
document.write( "         6 + Z = 6<BR>\n" );
document.write( "             Z = 6-6<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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ANSWER+TO+PROBLEM+A ALIGN=MIDDLE  ALT=\"ANSWER+TO+PROBLEM+A\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+2 ALIGN=MIDDLE  ALT=\"X+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+2 ALIGN=MIDDLE  ALT=\"Y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z+=+O ALIGN=MIDDLE  ALT=\"Z+=+O\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "PROBLEM B.\r<BR>\n" );
document.write( "\n" );
document.write( "GIVEN:\r<BR>\n" );
document.write( "\n" );
document.write( "    10X + Y + Z = 12  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    8X + 2Y + Z = 11  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 20X - 10Y - 2Z = 8   --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "REQUIRED: FIND X, Y AND Z\r<BR>\n" );
document.write( "\n" );
document.write( "   <BR>\n" );
document.write( "SOLUTION:<BR>\n" );
document.write( "MULTIPLY <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > WITH -1 AND ADD TO <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > TO ELIMINATE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "  -10X - Y -Z = -12 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >*(-1)<BR>\n" );
document.write( "    8X +2Y +Z =  11 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  _________________<BR>\n" );
document.write( "  -2X  + Y    =  -1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "      -2X + Y = -1  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+4 ALIGN=MIDDLE  ALT=\"Equation+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "FROM <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+4 ALIGN=MIDDLE  ALT=\"Equation+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "      -2X + Y = -1  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+4 ALIGN=MIDDLE  ALT=\"Equation+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "            Y = 2X-1 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "NOW MULTIPLY <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > WITH <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND ADD TO <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > TO ELIMINATE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "    16X +  4Y + 2Z = 22 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*(2)<BR>\n" );
document.write( "    20X - 10Y - 2Z = 8  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   ___________________<BR>\n" );
document.write( "    36X -  6Y      = 30<BR>\n" );
document.write( "  <BR>\n" );
document.write( "          36X - 6Y = 30 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+6 ALIGN=MIDDLE  ALT=\"Equation+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOW WE CAN SOLVE FOR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > USING <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > IN <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+6 ALIGN=MIDDLE  ALT=\"Equation+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "          36X - 6Y = 30 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+6 ALIGN=MIDDLE  ALT=\"Equation+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "     36X - 6(2X-1) = 30 <BR>\n" );
document.write( "      36X -12X + 6 = 30<BR>\n" );
document.write( "               24X = 30-6 <BR>\n" );
document.write( "               24X = 24<BR>\n" );
document.write( "                 X = 24/24<BR>\n" );
document.write( "                 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+1 ALIGN=MIDDLE  ALT=\"X+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "NOW THAT HAVE HAVE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" >, WE CAN SOLVE FOR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" > USING <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "                 Y = 2X -1 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "                 Y = 2(1)-1<BR>\n" );
document.write( "                 Y = 2 - 1<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" );
document.write( "\n" );
document.write( "NOW THAT HAVE HAVE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, WE CAN SOLVE FOR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" > USING <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+%0D%0A%0D%0A3 ALIGN=MIDDLE  ALT=\"Equation+%0D%0A%0D%0A3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, LETS TRY <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "       10X + Y + Z = 12  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "     10(1) + 1 + Z = 12<BR>\n" );
document.write( "       10  + 1 + Z = 12<BR>\n" );
document.write( "            11 + Z = 12<BR>\n" );
document.write( "                 Z = 12-11<BR>\n" );
document.write( "                 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z+=+1 ALIGN=MIDDLE  ALT=\"Z+=+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=ANSWER+TO+PROBLEM+B ALIGN=MIDDLE  ALT=\"ANSWER+TO+PROBLEM+B\"   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+=+1 ALIGN=MIDDLE  ALT=\"X+=+1\"   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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z+=+1 ALIGN=MIDDLE  ALT=\"Z+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "PROBLEM C \r<BR>\n" );
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document.write( "GIVEN:\r<BR>\n" );
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document.write( "22X + 5Y + 7Z  = 12 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "10X + 3Y + 2Z  = 5  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 9X + 2Y + 12Z = 14 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "REQUIRED: FIND X, Y AND Z\r<BR>\n" );
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document.write( "SOLUTION:\r<BR>\n" );
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document.write( "MULTIPLY <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > WITH <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND ADD TO <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > TO ELIMINATE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( " -22X - 5Y - 7Z  = -12  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >*(-1)<BR>\n" );
document.write( "  10X + 3Y + 2Z  =   5  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   9X + 2Y + 12Z =  14  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  -3X      + 7Z  =   7\r<BR>\n" );
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document.write( "       -3X + 7Z  =  7   --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+4 ALIGN=MIDDLE  ALT=\"Equation+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "FROM <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+4 ALIGN=MIDDLE  ALT=\"Equation+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "       -3X + 7Z  =  7   --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+4 ALIGN=MIDDLE  ALT=\"Equation+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "              3X = 7Z - 7   <BR>\n" );
document.write( "               X = (7Z -7)/3  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "MULTIPLY <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > WITH <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%283%2F2%29 ALIGN=MIDDLE  ALT=\"-%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND ADD TO <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > TO ELIMINATE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( " -(27/2)x  - 3Y  - 18z  = -21  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+3 ALIGN=MIDDLE  ALT=\"Equation+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > * (-3/2) <BR>\n" );
document.write( "      10X  + 3Y  +  2Z  =   5  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   _________________________<BR>\n" );
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document.write( "  (-7/2)x        - 16z  = -16 \r<BR>\n" );
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document.write( "         (-7/2)x - 16z  = -16 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+7 ALIGN=MIDDLE  ALT=\"Equation+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "FROM <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+7 ALIGN=MIDDLE  ALT=\"Equation+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "        [(-7/2)x - 16z  =  -16] * 2 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+7 ALIGN=MIDDLE  ALT=\"Equation+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >*2<BR>\n" );
document.write( "              -7X - 32Z = -32  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+8 ALIGN=MIDDLE  ALT=\"Equation+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOW WE CAN SOLVE FOR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > USING <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > IN <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+8 ALIGN=MIDDLE  ALT=\"Equation+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "               7X - 32Z = -32  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+8 ALIGN=MIDDLE  ALT=\"Equation+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "     -7[(7Z-7)/3] - 32Z = -32<BR>\n" );
document.write( "   [(-49Z + 49)/3 - 32Z = -32] *3 <BR>\n" );
document.write( "        -49Z + 49 - 96Z = -96<BR>\n" );
document.write( "                  -145Z = -145<BR>\n" );
document.write( "                      Z = -145/-145<BR>\n" );
document.write( "                      <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z+=+1 ALIGN=MIDDLE  ALT=\"Z+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOW THAT WE HAVE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" > WE CAN SOLVE FOR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X ALIGN=MIDDLE  ALT=\"X\"   DISABLED_style= \"max-width:90%; height:auto;\" > USING <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "                      X = (7Z -7)/3  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+5 ALIGN=MIDDLE  ALT=\"Equation+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "                      X = [7(1) - 7]/3<BR>\n" );
document.write( "                      X = (7-7)/3<BR>\n" );
document.write( "                      X = 0/3<BR>\n" );
document.write( "                      <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+0 ALIGN=MIDDLE  ALT=\"X+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOW THAT HAVE HAVE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z ALIGN=MIDDLE  ALT=\"Z\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, WE CAN SOLVE FOR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" > USING <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+2 ALIGN=MIDDLE  ALT=\"Equation+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+%0D%0A%0D%0A3 ALIGN=MIDDLE  ALT=\"Equation+%0D%0A%0D%0A3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, LETS TRY <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "         22X + 5Y + 7Z  = 12 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Equation+1 ALIGN=MIDDLE  ALT=\"Equation+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "      22(0) + 5Y + 7(1) = 12<BR>\n" );
document.write( "             0 + 5Y + 7 = 12<BR>\n" );
document.write( "                     5Y = 12-7<BR>\n" );
document.write( "                     5Y = 5<BR>\n" );
document.write( "                      Y = 5/5<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=X+=+0 ALIGN=MIDDLE  ALT=\"X+=+0\"   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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z+=+1 ALIGN=MIDDLE  ALT=\"Z+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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