document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148619>Question 148619</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this problem using the Gaussian Elimination method step by step please!\r<BR>\n" );
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document.write( "4x+3y+2z=6<BR>\n" );
document.write( "-2x-y+5z=5<BR>\n" );
document.write( "x+2y-3z=3\r<BR>\n" );
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document.write( "thank you in advance!<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 #109055 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y%2B2z=6 ALIGN=MIDDLE  ALT=\"4x%2B3y%2B2z=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-y%2B5z=5 ALIGN=MIDDLE  ALT=\"-2x-y%2B5z=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y-3z=3 ALIGN=MIDDLE  ALT=\"x%2B2y-3z=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine equations to remove one of the variables. <BR>\n" );
document.write( "Multiply eq. 2 by (3) and add to eq. 1,<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28-2x-y%2B5z%29=3%285%29 ALIGN=MIDDLE  ALT=\"3%28-2x-y%2B5z%29=3%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-3y%2B15z=15 ALIGN=MIDDLE  ALT=\"-6x-3y%2B15z=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This gets rid of y and makes a new eq. 1 with just x and z,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y%2B2z-6x-3y%2B15z=6%2B15 ALIGN=MIDDLE  ALT=\"4x%2B3y%2B2z-6x-3y%2B15z=6%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2B17z=21 ALIGN=MIDDLE  ALT=\"-2x%2B17z=21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply eq. 2 by (2) and add to eq. 3,<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-2x-y%2B5z%29=2%285%29 ALIGN=MIDDLE  ALT=\"2%28-2x-y%2B5z%29=2%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-2y%2B10z%29=10 ALIGN=MIDDLE  ALT=\"-4x-2y%2B10z%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This gets rid of y and makes a new eq. 3 with just x and z,<BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y-3z-4x-2y%2B10z=3%2B10 ALIGN=MIDDLE  ALT=\"x%2B2y-3z-4x-2y%2B10z=3%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B7z=13 ALIGN=MIDDLE  ALT=\"-3x%2B7z=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have two equations in x and z.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2B17z=21 ALIGN=MIDDLE  ALT=\"-2x%2B17z=21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B7z=13 ALIGN=MIDDLE  ALT=\"-3x%2B7z=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can continue to reduce to one variable. <BR>\n" );
document.write( "Multiply eq. 1 by 3 and eq. 3 by -2 and add them to get rid of x,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28-2x%2B17z%29=3%2821%29 ALIGN=MIDDLE  ALT=\"3%28-2x%2B17z%29=3%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B51z=63 ALIGN=MIDDLE  ALT=\"-6x%2B51z=63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28-3x%2B7z%29=-2%2813%29 ALIGN=MIDDLE  ALT=\"-2%28-3x%2B7z%29=-2%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-14z=-26 ALIGN=MIDDLE  ALT=\"6x-14z=-26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now add the two eqs.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B51z%2B6x-14z=63-26 ALIGN=MIDDLE  ALT=\"-6x%2B51z%2B6x-14z=63-26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37z=37 ALIGN=MIDDLE  ALT=\"37z=37\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=1 ALIGN=MIDDLE  ALT=\"z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now that you have z, work backwards and back substitute to find x and then y.<BR>\n" );
document.write( "You can use any of the previous equations to solve for other variables.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B7z=13 ALIGN=MIDDLE  ALT=\"-3x%2B7z=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B7%281%29=13 ALIGN=MIDDLE  ALT=\"-3x%2B7%281%29=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B7=13 ALIGN=MIDDLE  ALT=\"-3x%2B7=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x=6 ALIGN=MIDDLE  ALT=\"-3x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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( "And finally for y,<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-y%2B5z=5 ALIGN=MIDDLE  ALT=\"-2x-y%2B5z=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28-2%29-y%2B5%281%29=5 ALIGN=MIDDLE  ALT=\"-2%28-2%29-y%2B5%281%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-y%2B5=5 ALIGN=MIDDLE  ALT=\"4-y%2B5=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(x,y,z)=(-2,4,1) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );