document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174549>Question 174549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . Solve for X, Y, and Z in the following systems of three equations:<BR>\n" );
document.write( "a. X + 2Y + Z = 6<BR>\n" );
document.write( "    X + Y  = 4<BR>\n" );
document.write( "    3X + Y + Z =  8<BR>\n" );
document.write( "b. 10X + Y + Z = 12<BR>\n" );
document.write( "    8X + 2Y +Z  = 11<BR>\n" );
document.write( "    20X - 10Y - 2Z = 8<BR>\n" );
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 #129637 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=129637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I did this one already.  You can see how it's done and do the other 2.<BR>\n" );
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document.write( "Solve for X, Y, and Z in the following equations: <BR>\n" );
document.write( "22X + 5Y + 7Z = 12<BR>\n" );
document.write( "10X + 3Y + 2Z = 5<BR>\n" );
document.write( "9X + 2Y + 12Z = 14 <BR>\n" );
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document.write( "To use elimination methods, you have to pick one of the 3 variables to be eliminated that will give you 2 eqns in 2 unknowns. In these 3, y has the smallest coefficients, so I'd pick it and use the 3rd eqn to subtract from the other two, since its coeff is 2.<BR>\n" );
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document.write( "Multiply eqn 3 by 5 and eqn 1 by 2<BR>\n" );
document.write( "44x + 10y + 14z = 24 from eqn 1<BR>\n" );
document.write( "45x + 10y + 60z = 70 from eqn 3. Subtract 1 from 3<BR>\n" );
document.write( "x + 46z = 46 That's one.<BR>\n" );
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document.write( "Now multiply eqn 3 x3 and eqn 2 x2<BR>\n" );
document.write( "20x + 6y + 4z = 10 from eqn 2<BR>\n" );
document.write( "27x + 6y + 36z = 42 from eqn 3 Subtract 2 from 3 (to give pos coeffs)<BR>\n" );
document.write( "7x + 32z = 32 That's the 2nd eqn in x and z only.<BR>\n" );
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document.write( "7x + 32z = 32 Multiply the other one by 7<BR>\n" );
document.write( "7x + 322z = 322<BR>\n" );
document.write( "Subtract<BR>\n" );
document.write( "-290z = -290<BR>\n" );
document.write( "z = 1<BR>\n" );
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document.write( "Sub into either of the 2 variable eqns<BR>\n" );
document.write( "7x + 32*1 = 32<BR>\n" );
document.write( "7x = 0<BR>\n" );
document.write( "x = 0<BR>\n" );
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document.write( "Now sub into the original eqn 3<BR>\n" );
document.write( "9X + 2Y + 12Z = 14 <BR>\n" );
document.write( "9*0 + 2y + 12*1 = 14<BR>\n" );
document.write( "2y = 2<BR>\n" );
document.write( "y = 1<BR>\n" );
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document.write( "So it's 0, 1, 1 for x, y, z<BR>\n" );
document.write( "The important thing to remember is to eliminate one variable first, then another, etc.  </SPAN>\n" );
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