document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=111134>Question 111134</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve for x, y, z.  I understand how to solve for two variables but I don't understand how to solve for three.  \r<BR>\n" );
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document.write( "Solve for x, y, and z.<BR>\n" );
document.write( "X + Y + 2Z =5<BR>\n" );
document.write( "X + Y =5<BR>\n" );
document.write( "X + 3Y + Z =11<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 #81085 by </B><A HREF=/tutors/aboutme.mpl?userid=dolly><B>dolly(163)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dolly><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=81085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello\r<BR>\n" );
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document.write( "Solving for 3 variables is similar to solving for 2 variables except that you have to reduce these to 2 equations with 2 similar variables.\r<BR>\n" );
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document.write( "Given X + Y + 2Z =5 -----------(1)<BR>\n" );
document.write( "X + Y =5 -------------------(2)<BR>\n" );
document.write( "X + 3Y + Z =11 ----------------(3)\r<BR>\n" );
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document.write( "(3) * 2 gives 2X + 6Y + 2Z = 22 --------------(4)\r<BR>\n" );
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document.write( "               X + Y + 2Z = 5 ----------------(1)\r<BR>\n" );
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document.write( "Subtracting (1) from (4) gives, <BR>\n" );
document.write( "  X + 5Y = 17 ---------------(5)<BR>\n" );
document.write( "  X + Y = 5 ---------------(2)\r<BR>\n" );
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document.write( "Subtracting (2) from (5) gives, 4Y = 12<BR>\n" );
document.write( "                                Y = 12/ 4<BR>\n" );
document.write( "                                Y = 3\r<BR>\n" );
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document.write( "Plugging this value of Y in (2),<BR>\n" );
document.write( "X + 3 = 5<BR>\n" );
document.write( "==> X = 5 - 3<BR>\n" );
document.write( "==> X = 2\r<BR>\n" );
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document.write( "Substituting these values in (3) gives,<BR>\n" );
document.write( "2 + 3(3) + Z = 11<BR>\n" );
document.write( "==> 2 + 9 + Z = 11<BR>\n" );
document.write( "==> 11 + Z = 11<BR>\n" );
document.write( "==> Z = 11 - 11<BR>\n" );
document.write( "==> Z = 0\r<BR>\n" );
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document.write( "Thus X = 2;   Y = 3;   Z = 0 \r<BR>\n" );
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document.write( "Best of Luck!!! </SPAN>\n" );
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