document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202709>Question 202709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7. Solve for X,Y and Z<BR>\n" );
document.write( "2X+2Y+4Z=10<BR>\n" );
document.write( "3X+3Y=15<BR>\n" );
document.write( "4X+12Y+4Z=44<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 #152948 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=152948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2X+2Y+4Z=10<BR>\n" );
document.write( "3X+3Y=15<BR>\n" );
document.write( "4X+12Y+4Z=44\r<BR>\n" );
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document.write( "Let's take two equations and eliminate one variable.  I'd suggest the variable \"Z\" because the 2nd equation does not have a \"z\".  SO, let's work with equation 1 and 3....\r<BR>\n" );
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document.write( "To get rid of the \"Z\" variable, let's multiply this equation 4X+12Y+4Z=44 by a negative 1.   \r<BR>\n" );
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document.write( "2X+2Y+4Z=10<BR>\n" );
document.write( "4X+12Y+4Z=44  (multiply by -1)\r<BR>\n" );
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document.write( "Two new equations....<BR>\n" );
document.write( "2X  + 2Y+ 4Z =  10<BR>\n" );
document.write( "-4x -12y -4z = -44<BR>\n" );
document.write( "_________________  now add these two equations<BR>\n" );
document.write( "-2x - 10y    = -34\r<BR>\n" );
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document.write( "Now let's take this new equation and look at it along with the other equation that only had \"X\" and \"Y\" variables.........\r<BR>\n" );
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document.write( "-2x - 10y = -34  (What if we multiply this by 3?)<BR>\n" );
document.write( "3X + 3Y = 15  (What if we multiply this by 2?)\r<BR>\n" );
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document.write( "If we do the multiplications I suggest above, our new equations will be:\r<BR>\n" );
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document.write( "-6x -30y =   -102<BR>\n" );
document.write( "6x + 6y = 30<BR>\n" );
document.write( "_________________ add these equations<BR>\n" );
document.write( "    -24y = -72  (divide both sides by -24)\r<BR>\n" );
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document.write( "y = 3\r<BR>\n" );
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document.write( "Now that we know what Y is, let's plug it into the equation with only 2 variables...........\r<BR>\n" );
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document.write( "3X+3Y=15<BR>\n" );
document.write( "3x+3(3) = 15 (plug in the 3 for the y variable)<BR>\n" );
document.write( "3x + 9 = 15  (multiply 3 times 3)<BR>\n" );
document.write( "3x = 6  (subtract 9 from both sides)<BR>\n" );
document.write( "x =2 (divide both sides by 3)\r<BR>\n" );
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document.write( "Ok, now we know x = 2 and y = 3.  Let's plug those numbers into one of the equations that has three variables.  I will choose the first equation:\r<BR>\n" );
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document.write( "2X+2Y+4Z=10<BR>\n" );
document.write( "2(2) + 2(3) + 4z = 10 (plug in 2 for the x variable and 3 for the y variable)<BR>\n" );
document.write( "4 + 6+ 4z = 10 (multiply 2 times 2.  Multiply 2 times 3)<BR>\n" );
document.write( "10 + 4z = 10 (added 4 and 6)<BR>\n" );
document.write( "4z = 0 (subtracted 10 from both sides)<BR>\n" );
document.write( "z = 0 (divided both sides by 4)\r<BR>\n" );
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document.write( "Now we know x = 2, y = 3 and z = 0.  If we plug these into our 3 equations, will they all check out?  Let's try it:\r<BR>\n" );
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document.write( "First equation:<BR>\n" );
document.write( "2X+2Y+4Z=10<BR>\n" );
document.write( "2(2) + 2(3) + 4(0) = 10<BR>\n" );
document.write( "4 + 6 + 0 = 10<BR>\n" );
document.write( "10= 10  <BR>\n" );
document.write( "Yay... the 1st equation works.\r<BR>\n" );
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document.write( "Second equation:<BR>\n" );
document.write( "3X+3Y=15<BR>\n" );
document.write( "3(2) + 3(3) = 15<BR>\n" );
document.write( "6 + 9 = 15<BR>\n" );
document.write( "15 = 15<BR>\n" );
document.write( "Yay... the 2nd equation works. :-) Let's go for the 3rd.......\r<BR>\n" );
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document.write( "Third equation:<BR>\n" );
document.write( "4X+12Y+4Z=44<BR>\n" );
document.write( "4(2) + 12(3) + 4(0)=44<BR>\n" );
document.write( "8 + 36 + 0 = 44<BR>\n" );
document.write( "44 = 44<BR>\n" );
document.write( "Yay... the 3rd equation works.  SO cool.  \r<BR>\n" );
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document.write( "Hope this helps...    :-) </SPAN>\n" );
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