document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=313259>Question 313259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello I have a problem, but cant seem to find out what i am doing wrong. The equations are solutions to systems of linear equations in three variables.\r<BR>\n" );
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document.write( "2x+ y-3z=-12<BR>\n" );
document.write( "3x-2y-z=  3<BR>\n" );
document.write( "-x+5y+2z=-3\r<BR>\n" );
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document.write( "I know you have to work only two equations at a time. My teacher took the class through it step by step but i'm thinking im making a mistake on my adding or subtracting because i keep coming out with the wrong answer.<BR>\n" );
document.write( "THanks <BR>\n" );
document.write( "Kayla </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224012 by </B><A HREF=/tutors/aboutme.mpl?userid=OmniMaestra><B>OmniMaestra(21)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=OmniMaestra><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=OmniMaestra><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=224012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x+ y-3z=-12<BR>\n" );
document.write( "3x-2y-z=  3<BR>\n" );
document.write( "-x+5y+2z=-3\r<BR>\n" );
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document.write( "Yes, you do have to take it 2 equations at a time. THere are some options to begin so we look for the option that will make our work easy.\r<BR>\n" );
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document.write( "I'm going to start with the first two equations and eliminate the y.\r<BR>\n" );
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document.write( "I'll multiply the first equation by 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B2y-6z=-24 ALIGN=MIDDLE  ALT=\"4x%2B2y-6z=-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y-_z=__3 ALIGN=MIDDLE  ALT=\"3x-2y-_z=__3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now I add down:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x+-7z=-21 ALIGN=MIDDLE  ALT=\"7x+-7z=-21\"   DISABLED_style= \"max-width:90%; height:auto;\" >....Since all the terms are divisible by 7, I will simplify by dividing by 7\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-z=-3 ALIGN=MIDDLE  ALT=\"x-z=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, I must eliminate the y's with a different set of two equations.<BR>\n" );
document.write( "I'm going to do the first and third equations.\r<BR>\n" );
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document.write( "2x+ y-3z=-12<BR>\n" );
document.write( "-x+5y+2z=-3\r<BR>\n" );
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document.write( "Multiply the top equation by -5. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10x-5y%2B15z=60 ALIGN=MIDDLE  ALT=\"-10x-5y%2B15z=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-__x%2B5y%2B_2z=-3 ALIGN=MIDDLE  ALT=\"-__x%2B5y%2B_2z=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add down:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11x%2B17z=57 ALIGN=MIDDLE  ALT=\"-11x%2B17z=57\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Use the two new equations and eliminate the x's<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=___x-__z=-3 ALIGN=MIDDLE  ALT=\"___x-__z=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets eliminate the z's.<BR>\n" );
document.write( "Multiply the second equation by 17.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11x%2B17z=57 ALIGN=MIDDLE  ALT=\"-11x%2B17z=57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=_17x-17z=-51 ALIGN=MIDDLE  ALT=\"_17x-17z=-51\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "add down:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=6 ALIGN=MIDDLE  ALT=\"6x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "divide by 6<BR>\n" );
document.write( "<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;\" >\r<BR>\n" );
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document.write( "I'm going to use the two equations I created when I eliminated the y's and substitute 1 in place of the x's. Then solve both for z.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11x%2B17z=57 ALIGN=MIDDLE  ALT=\"-11x%2B17z=57\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%2A1%2B17z=57 ALIGN=MIDDLE  ALT=\"-11%2A1%2B17z=57\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17z=57%2B11 ALIGN=MIDDLE  ALT=\"17z=57%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> divide by 17. z= 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=___x-__z=-3 ALIGN=MIDDLE  ALT=\"___x-__z=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=____1-__z=-3 ALIGN=MIDDLE  ALT=\"____1-__z=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-z=-4 ALIGN=MIDDLE  ALT=\"+-z=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=4 ALIGN=MIDDLE  ALT=\"z=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you know that x=1 and z=4. Use one of the original equations, substitute, then solve for y.\r<BR>\n" );
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document.write( "-x+5y+2z=-3<BR>\n" );
document.write( "-1+5y+2*4=-3<BR>\n" );
document.write( "-1+5y+8=-3<BR>\n" );
document.write( "5y+7=-3<BR>\n" );
document.write( "5y=-10<BR>\n" );
document.write( "y=-2\r<BR>\n" );
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document.write( "x=1<BR>\n" );
document.write( "y=-2<BR>\n" );
document.write( "z=4 </SPAN>\n" );
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