document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=2157>Question 2157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please solve for X, Y, and Z in the 3 variable equation.\r<BR>\n" );
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document.write( "x + 2y + z =6<BR>\n" );
document.write( "x + y =4<BR>\n" );
document.write( "3x + y + z =8 <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 #879 by </B><A HREF=/tutors/aboutme.mpl?userid=matthew_sessoms><B>matthew_sessoms(39)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=matthew_sessoms><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=879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets number each equation so we can refer to each one with only a number (instead of writing the whole equation).<BR>\n" );
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document.write( "1)  x + 2y + z = 6<BR>\n" );
document.write( "2)  x +  y     = 4<BR>\n" );
document.write( "3) 3x +  y + z = 8<BR>\n" );
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document.write( "Now lets eliminate 1 (one) variable from from all the equations.  Lets start with only 2 equations at a time.  I will eliminate x from #1 & #2 first.<BR>\n" );
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document.write( "(-1) * #1 = -x - 2y - z = -6<BR>\n" );
document.write( "       #2 =  x +  y     = 4<BR>\n" );
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document.write( "Then add these, and we will get equation #4, like this<BR>\n" );
document.write( "#4 = -y - z = -2<BR>\n" );
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document.write( "Now, lets eliminate the SAME variable (x) from equation #1 & #3 (since before, we eliminated x from #1 & #2)<BR>\n" );
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document.write( "(-3) * #1 = -3x - 6y - 3z = -18<BR>\n" );
document.write( "       #3 =  3x +  y +  z =   8<BR>\n" );
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document.write( "Add these, and we get equation #5, which is<BR>\n" );
document.write( "#5 = -5y - 2z = -10<BR>\n" );
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document.write( "All we have now is 2 equations with 2 variables (#4 & #5).  We can use \"substitution to solve for y in #4 and plug it in #5.<BR>\n" );
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document.write( "#4 = y = 2 - z<BR>\n" );
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document.write( "Now plug in #4, which we solved for y, into #5 and simplify.<BR>\n" );
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document.write( "-5(2 - z) - 2z = -10<BR>\n" );
document.write( "<b>z = 0</b><BR>\n" );
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document.write( "Now, plug in z=0 in either #4 or #5.  I chosed #4 because it looks easier.<BR>\n" );
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document.write( "-y - 0 = -2<BR>\n" );
document.write( "<b>y = 2</b><BR>\n" );
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document.write( "Now, since we have y & z, we can plug these values into either of the original equations (#1, #2, or #3).  I chosed #1 because it looks easier.<BR>\n" );
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document.write( "x + 2(2) + 0 = 6<BR>\n" );
document.write( "<b>x = 2</b><BR>\n" );
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document.write( "Now we have our final answer, <b> (2, 2, 0)</b>, as in (x, y, z).<BR>\n" );
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document.write( "CHECK<BR>\n" );
document.write( "#1. 2 + 2(2) + 0 = 6<BR>\n" );
document.write( "#2. 2 + 2 = 4<BR>\n" );
document.write( "#3. 3(2) + 2 + 0 = 8<BR>\n" );
document.write( "MS </SPAN>\n" );
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