document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=2240>Question 2240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ok this is my last problem. That you so much!\r<BR>\n" );
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document.write( "Solve for X,Y,and Z in the following  systems of three equations:\r<BR>\n" );
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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 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #933 by </B><A HREF=/tutors/aboutme.mpl?userid=DeepaEvangeline><B>DeepaEvangeline(15)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DeepaEvangeline><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=933\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)<BR>\n" );
document.write( "X+2Y+Z=6 - (1)<BR>\n" );
document.write( "X+Y=4    - (2)<BR>\n" );
document.write( "3X+Y+Z=8 - (3)\r<BR>\n" );
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document.write( "Eqn(3) - Eqn(1) gives<BR>\n" );
document.write( "2X-Y=2   - (4)\r<BR>\n" );
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document.write( "Adding Eqn(2) & (4) gives<BR>\n" );
document.write( "3X=6 -> X = 2\r<BR>\n" );
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document.write( "Substituting the value of X in eqn(2) gives<BR>\n" );
document.write( "X+Y=4<BR>\n" );
document.write( "2+Y=4 -> Y = 2\r<BR>\n" );
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document.write( "Sub the value of X=2 and Y=2 in eqn (1) gives<BR>\n" );
document.write( "2+2.2+Z=6<BR>\n" );
document.write( "2+4+Z=6 -> Z = 0\r<BR>\n" );
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document.write( "X = 2, Y = 2, Z = 0\r<BR>\n" );
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document.write( "b)<BR>\n" );
document.write( "10X+Y+Z=12  - (1)<BR>\n" );
document.write( "8X+2Y+Z=11  - (2)<BR>\n" );
document.write( "20X-10Y-2Z=8 - (3)\r<BR>\n" );
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document.write( "Subtracting eqn(2) from eqn(1) gives<BR>\n" );
document.write( "2X-Y=1  - (4)\r<BR>\n" );
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document.write( "Eqn(2) x 2 gives<BR>\n" );
document.write( "16X+4Y+2Z=22  - (5)\r<BR>\n" );
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document.write( "Eqn(3) + Eqn(5) gives<BR>\n" );
document.write( "36X-6Y=30  - (6)\r<BR>\n" );
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document.write( "Eqn(4) x 6 gives<BR>\n" );
document.write( "12X-6Y=6  - (7)\r<BR>\n" );
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document.write( "Eqn(6) - Eqn(7) gives<BR>\n" );
document.write( "24X=24 => X = 1\r<BR>\n" );
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document.write( "Substituting X = 1 in eqn(4) gives<BR>\n" );
document.write( "2.1-Y=1 => Y = 1\r<BR>\n" );
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document.write( "Sub the value of X = 1 and Y = 1 in eqn(1) gives<BR>\n" );
document.write( "10.1 + 1 + Z = 12<BR>\n" );
document.write( "11 + Z = 12 => Z = 1\r<BR>\n" );
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document.write( "X = 1, Y = 1, Z = 1\r<BR>\n" );
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document.write( "c)<BR>\n" );
document.write( "22X+5Y+7Z=12  - (1)<BR>\n" );
document.write( "10X+3Y+2Z=5   - (2)<BR>\n" );
document.write( "9X+2Y+12Z=14  - (3)\r<BR>\n" );
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document.write( "Eqn(1) x 3 gives<BR>\n" );
document.write( "66X+15Y+21Z=36  - (4)\r<BR>\n" );
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document.write( "Eqn(2) x 5 gives<BR>\n" );
document.write( "50X+15Y+10Z=25  - (5)\r<BR>\n" );
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document.write( "Eqn(4) - eqn(5) gives<BR>\n" );
document.write( "16X+11Z=11  - (6)\r<BR>\n" );
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document.write( "Eqn(2) x 2 gives<BR>\n" );
document.write( "20X+6Y+4Z=10  - (7)\r<BR>\n" );
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document.write( "Eqn(3) x 3 gives<BR>\n" );
document.write( "27X+6Y+36Z=42  - (8)\r<BR>\n" );
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document.write( "Eqn(8) - eqn(7) gives<BR>\n" );
document.write( "7X+32Z=32  - (9)\r<BR>\n" );
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document.write( "Solving eqn(6) & (9),<BR>\n" );
document.write( "Eqn(6) x 7 gives<BR>\n" );
document.write( "112X+77Z=77  - (10)\r<BR>\n" );
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document.write( "Eqn(9) x 16 gives<BR>\n" );
document.write( "112X+512Z=512  - (11)\r<BR>\n" );
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document.write( "Eqn(11) - eqn(10) gives<BR>\n" );
document.write( "435Z=435 => Z = 1\r<BR>\n" );
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document.write( "Substituting Z = 1 in eqn(9) gives<BR>\n" );
document.write( "7X+32=32 => X = 0\r<BR>\n" );
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document.write( "Sub X = 0 and Z = 1 in eqn(2) gives<BR>\n" );
document.write( "10.0 + 3Y + 2.1 = 5<BR>\n" );
document.write( "3Y = 3 => Y = 1\r<BR>\n" );
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document.write( "X = 0, Y = 1, Z = 1 </SPAN>\n" );
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