document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475310>Question 475310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x + 4y + 4z = 16<BR>\n" );
document.write( "2x -  y + 3z = 9<BR>\n" );
document.write( "3x + 4y -  z = 8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #325930 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=325930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think the best way to do these is using the elimination method.<BR>\n" );
document.write( "Eliminate a variable to break it down into a system of 2 equations, then use elimination again to break it down to a single equation. Solve for that variable and then use substitution to find the 2nd variable in the system of 2 equations. Then substitute both those values into one of the original equations to find 3rd variable. <BR>\n" );
document.write( "Let me label each equation: A,B,C for reference<BR>\n" );
document.write( "A:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+4y+%2B+4z+=+16 ALIGN=MIDDLE  ALT=\"2x+%2B+4y+%2B+4z+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+y+%2B+3z+=+9 ALIGN=MIDDLE  ALT=\"2x+-+y+%2B+3z+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+4y+-+z+=+8 ALIGN=MIDDLE  ALT=\"3x+%2B+4y+-+z+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice A and C both have a 4y, therefore it will be easiest to eliminate variable y. Multiply C by -1. Add A and C. Call the resulting equation D.<BR>\n" );
document.write( "D:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+5z+=+8 ALIGN=MIDDLE  ALT=\"-x+%2B+5z+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We still need another equation with x and z. To eliminate y again. Multiply B by 4. Add A and B. Call the resulting equation E.<BR>\n" );
document.write( "E:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x+%2B+16z+=+52 ALIGN=MIDDLE  ALT=\"10x+%2B+16z+=+52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now eliminate x. Multiply D by 10. Add D and E.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66z+=+132 ALIGN=MIDDLE  ALT=\"66z+=+132\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for z. Divide by 66 on both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+2 ALIGN=MIDDLE  ALT=\"z+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute z=2 into D.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+5%282%29+=+8 ALIGN=MIDDLE  ALT=\"-x+%2B+5%282%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for x. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+10+=+8 ALIGN=MIDDLE  ALT=\"-x+%2B+10+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 10 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+=+-2 ALIGN=MIDDLE  ALT=\"-x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Flip signs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute x=2, z=2 into B.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%282%29+-+y+%2B+3%282%29+=+9 ALIGN=MIDDLE  ALT=\"2%282%29+-+y+%2B+3%282%29+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+-+y+%2B+6+=+9 ALIGN=MIDDLE  ALT=\"4+-+y+%2B+6+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y+%2B+10+=+9 ALIGN=MIDDLE  ALT=\"-y+%2B+10+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 10 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y+=+-1 ALIGN=MIDDLE  ALT=\"-y+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Flip signs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1 ALIGN=MIDDLE  ALT=\"y+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Verify solution by substituting into other equations A and C.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%282%29+%2B+4%281%29+%2B+4%282%29+=+16 ALIGN=MIDDLE  ALT=\"2%282%29+%2B+4%281%29+%2B+4%282%29+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B4%2B8+=+16 ALIGN=MIDDLE  ALT=\"4%2B4%2B8+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+16 ALIGN=MIDDLE  ALT=\"16+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True...it works.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%282%29+%2B+4%281%29+-+2+=+8 ALIGN=MIDDLE  ALT=\"3%282%29+%2B+4%281%29+-+2+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+%2B+4+-+2=+8 ALIGN=MIDDLE  ALT=\"6+%2B+4+-+2=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=8 ALIGN=MIDDLE  ALT=\"8=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True..it works.<BR>\n" );
document.write( "Solution is x = 2, y = 1, z = 2<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );