document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=378503>Question 378503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve the following system of linear equations with three variables.<BR>\n" );
document.write( "Here is the system:\r<BR>\n" );
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document.write( "            2x-4y+3z=17<BR>\n" );
document.write( "             x+2y-z =0<BR>\n" );
document.write( "            4x -y -z=6\r<BR>\n" );
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document.write( "O.K. I know i need to reduce it to a system of 2 equations with 2 variables. This is what i have so far. I'm not certain it's right. I did this:\r<BR>\n" );
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document.write( "            2x-4y+3z.....2x-4y+3z=17<BR>\n" );
document.write( "           3(x+2y-z=0)...3x+6y-3z=0<BR>\n" );
document.write( "That got rid of my \"z\". now i THINK i\"m supposed to add? That gives me:\r<BR>\n" );
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document.write( "            5x+2y=17. O>K> There's my 1st equation with 2 variables. Now for the 2nd one.\r<BR>\n" );
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document.write( "          I did: x+2y-z (that's equation #2 in the original)<BR>\n" );
document.write( "                -1(4x-y-z=6)...I multiplied the original 3rd equation by -1 to get rid of ITS \"z\". I got:\r<BR>\n" );
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document.write( "                 -3x+3y=-6. There's my 2nd 2-variable equation. Now I did:<BR>\n" );
document.write( "               \r<BR>\n" );
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document.write( "      5x+2y=17<BR>\n" );
document.write( "      -3x+3y=-6...Now to solve: I chose to get rid of \"y\" and solve for x like this:\r<BR>\n" );
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document.write( "       -3(5x+2y=17)...-15x-6y=-57<BR>\n" );
document.write( "        2(-3x+3y=-6)..-6x+6y=-12<BR>\n" );
document.write( "Adding...............................<BR>\n" );
document.write( "                        21x  =-69<BR>\n" );
document.write( "                           69/21<BR>\n" );
document.write( "                           x=3.29 or 3<BR>\n" );
document.write( "My two questions are: A) is this right up til now? and B)What do i do now? I'm lost. Please help!:(\r<BR>\n" );
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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 #268874 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=268874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> YOU ARE DOING GREEEEAT!!!!!!!<BR>\n" );
document.write( "Down toward the end you have:<BR>\n" );
document.write( "-3(5x+2y=17)...-15x-6y=-57<BR>\n" );
document.write( "---and you made a simple error.  It should be.....-15x-6y=-51  (not 57)<BR>\n" );
document.write( "Now lets see how this changes the outcome<BR>\n" );
document.write( "Instead of --  -21x=-69 you have -21x=-63<BR>\n" );
document.write( "and x=3\r<BR>\n" );
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document.write( "Now the next step is to substitute x=3 into either of the equations with two unknowns and solve for y.  Then the next step would be to substitute the value you got for y plus the value you have for x (3) into either of the equations with 3 unknowns and then solve for z.\r<BR>\n" );
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document.write( "You are doing good---keep it up.\r<BR>\n" );
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document.write( "Hope this helps ---ptaylor  </SPAN>\n" );
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