document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=709251>Question 709251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP!!!!!!!!!!!!!!!!!!! \r<BR>\n" );
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document.write( "SOLVE FOR X <BR>\n" );
document.write( "2x + y + z = 0 <BR>\n" );
document.write( "3x - y + z = 3 <BR>\n" );
document.write( "7x - 5y - 3z = 15\r<BR>\n" );
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document.write( "thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436528 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=436528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282x+%2B+y+%2B+z+=+0%2C3x+-+y+%2B+z+=+3+%2C7x+-+5y+-+3z+=+15%29 ALIGN=MIDDLE  ALT=\"system%282x+%2B+y+%2B+z+=+0%2C3x+-+y+%2B+z+=+3+%2C7x+-+5y+-+3z+=+15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "I do not like the problem either, but no one answered yesterday, so I'll try today. (Warning: I make stupid mistakes in easy calculations, so watch for my mistakes)<BR>\n" );
document.write( "Probably you want to use the elimination method, and not matrices.<BR>\n" );
document.write( "You want to combine equations to get 2 combination equations with 2 variables.<BR>\n" );
document.write( "(We still have a 3-variable-3-equation system, but we can set aside one of the original equations, with all 3 variables, as our third equation, and not worry about it for now).<BR>\n" );
document.write( "Then, we would be able to solve the set of combination equations as a two-variable-two-equation system.<BR>\n" );
document.write( " <BR>\n" );
document.write( "It looks like the easiest way would be to use the simpler first equation,<BR>\n" );
document.write( "combining it with each of the other equations, to eliminate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Subtracting the first equation from the second one you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=3 ALIGN=MIDDLE  ALT=\"x-2y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the first equation to the third one you get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x-2y=15 ALIGN=MIDDLE  ALT=\"13x-2y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x-2y=3%2C13x-2y=15%29 ALIGN=MIDDLE  ALT=\"system%28x-2y=3%2C13x-2y=15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I would subtract the new system's first equation from the other equation to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x=12 ALIGN=MIDDLE  ALT=\"12x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=3 ALIGN=MIDDLE  ALT=\"x-2y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rather than into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x-2y=15 ALIGN=MIDDLE  ALT=\"13x-2y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) looks easy enough.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2y=3 ALIGN=MIDDLE  ALT=\"1-2y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y=3-1 ALIGN=MIDDLE  ALT=\"-2y=3-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y=2 ALIGN=MIDDLE  ALT=\"-2y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y%2F%28-2%29=2%2F%28-2%29 ALIGN=MIDDLE  ALT=\"-2y%2F%28-2%29=2%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Then, I would go back to one of the original equations and substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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;\" > to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I chose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+y+%2B+z+=+0 ALIGN=MIDDLE  ALT=\"2x+%2B+y+%2B+z+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the equation that looks easiest.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%281%29+%2B+%28-1%29+%2B+z+=+0 ALIGN=MIDDLE  ALT=\"2%281%29+%2B+%28-1%29+%2B+z+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1%2Bz=0 ALIGN=MIDDLE  ALT=\"2-1%2Bz=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bz=0 ALIGN=MIDDLE  ALT=\"1%2Bz=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28z=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28z=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I verified on my own on scrap paper and it seems to work,<BR>\n" );
document.write( "but remember, I warned you that I'm error prone. </SPAN>\n" );
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