document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203437>Question 1203437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3x+6y-z=7<BR>\n" );
document.write( "2x-3y+5z=-12<BR>\n" );
document.write( "8x+9y-2z=12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839006 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Solve the 1st equation for z.<BR>\n" );
document.write( "3x+6y-z = 7<BR>\n" );
document.write( "3x+6y = 7+z<BR>\n" );
document.write( "3x+6y-7 = z<BR>\n" );
document.write( "z = 3x+6y-7\r<BR>\n" );
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document.write( "Plug this into the 2nd equation.<BR>\n" );
document.write( "2x-3y+5z = -12<BR>\n" );
document.write( "2x-3y+5(3x+6y-7) = -12<BR>\n" );
document.write( "2x-3y+15x+30y-35 = -12<BR>\n" );
document.write( "17x+27y-35 = -12<BR>\n" );
document.write( "17x+27y = -12+35<BR>\n" );
document.write( "17x+27y = 23\r<BR>\n" );
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document.write( "Do the same for the 3rd equation.<BR>\n" );
document.write( "8x+9y-2z=12<BR>\n" );
document.write( "8x+9y-2(3x+6y-7)=12<BR>\n" );
document.write( "8x+9y-6x-12y+14=12<BR>\n" );
document.write( "2x-3y+14=12<BR>\n" );
document.write( "2x-3y=12-14<BR>\n" );
document.write( "2x-3y=-2\r<BR>\n" );
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document.write( "The task is now to solve this reduced system<BR>\n" );
document.write( "17x+27y = 23<BR>\n" );
document.write( "2x-3y = -2\r<BR>\n" );
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document.write( "We can solve for x in the equation 2x-3y = -2 to get x = 1.5y-1<BR>\n" );
document.write( "Then plug this into the other equation to solve for y<BR>\n" );
document.write( "17x+27y = 23<BR>\n" );
document.write( "17(1.5y-1)+27y = 23<BR>\n" );
document.write( "25.5y-17+27y = 23<BR>\n" );
document.write( "52.5y-17 = 23<BR>\n" );
document.write( "52.5y = 23+17<BR>\n" );
document.write( "52.5y = 40<BR>\n" );
document.write( "y = 40/52.5<BR>\n" );
document.write( "y = 400/525<BR>\n" );
document.write( "y = 16/21\r<BR>\n" );
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document.write( "Use this value of y to find x.<BR>\n" );
document.write( "Then use the values of x and y to find z.\r<BR>\n" );
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document.write( "I'll let the student take over from here.<BR>\n" );
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