document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=785389>Question 785389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to solve a linear equation with three variables and I am stuck on this problem. My teacher said the answer is not in a fraction but is a whole number but every time I have tried to solve it I get a fraction.\r<BR>\n" );
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document.write( "3x-2y+3z=11<BR>\n" );
document.write( "5x+2y-2z=4<BR>\n" );
document.write( "-x+y+z=-7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #477506 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=477506\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When my solution does not check, or looks too complicated, I throw away my prior attempt, take a few deep breaths, and start again from scratch writing as big and neatly as possible on a large, clean piece of paper. I did that with your problem, twice, and the third time was a charm. (If I reviewed what I had done looking for the mistake, I would be most likely to miss it).<BR>\n" );
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document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283x-2y%2B3z=11%2C5x%2B2y-2z=4%2C-x%2By%2Bz=-7%29 ALIGN=MIDDLE  ALT=\"system%283x-2y%2B3z=11%2C5x%2B2y-2z=4%2C-x%2By%2Bz=-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "-x+y+z=-7  looks like the simplest of the three equations.<BR>\n" );
document.write( "I am going to use it 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;\" > from the other two.<BR>\n" );
document.write( "(The sooner I 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;\" > the less likely I am to confuse it with a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
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document.write( "I multiply -x+y+z=-7 times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29 ALIGN=MIDDLE  ALT=\"%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and add it to 3x-2y+3z=11:<BR>\n" );
document.write( "3x -2y  +3z  =  11<BR>\n" );
document.write( "3x -3y  -3z  =  21<BR>\n" );
document.write( "______________<BR>\n" );
document.write( "6x -5y       =  32<BR>\n" );
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document.write( "I multiply -x+y+z=-7 times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and add it to 5x+2y-2z=4:<BR>\n" );
document.write( " 5x +2y  -2z  =  4<BR>\n" );
document.write( "-2x +2y  +2z  = -14<BR>\n" );
document.write( "______________<BR>\n" );
document.write( "3x +4y       =  -10<BR>\n" );
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document.write( "Now I have the equivalent system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-x%2By%2Bz=-7%2C6x-5y=32%2C3x%2B4y=-10%29 ALIGN=MIDDLE  ALT=\"system%28-x%2By%2Bz=-7%2C6x-5y=32%2C3x%2B4y=-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I am going to combine 6x-5y=32 and 3x+4y=-10 to get an equation without <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "I multiply 3x+4y=-10 times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29 ALIGN=MIDDLE  ALT=\"%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and add it to 6x-5y=32:<BR>\n" );
document.write( " 6x -5y  =  32<BR>\n" );
document.write( "-6x -8y  =  20<BR>\n" );
document.write( "___________<BR>\n" );
document.write( "-13y  =  52  ---------> y = 52 / (-13) -----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-4%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now I have the equivalent system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-x%2By%2Bz=-7%2C3x%2B4y=-10%2C+y=-4%29 ALIGN=MIDDLE  ALT=\"system%28-x%2By%2Bz=-7%2C3x%2B4y=-10%2C+y=-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substituting y=-4 into 3x+4y=-10, I get<BR>\n" );
document.write( "3x+4(-4)=-10  ------> 3x-16 = -10 ------> 3x=-10+16 ----> 3x=6 ---> x=6/3 ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now I have the equivalent system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-x%2By%2Bz=-7%2Cx=2%2C+y=-4%29 ALIGN=MIDDLE  ALT=\"system%28-x%2By%2Bz=-7%2Cx=2%2C+y=-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substituting x=2 and y= -4 into -x+y+z=-7, I get<BR>\n" );
document.write( "-2 + (-4) +z = -7 ---> -2-4 +z = -7 ---> -6 + z = -7 --> z=-7+6 ---> <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;\" > </SPAN>\n" );
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