document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159260>Question 159260</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a substitution problem that I would like help with, please (I have a test tomorrow).\r<BR>\n" );
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document.write( "x + y + z = 3<BR>\n" );
document.write( "3x + 3y + 3z = 10<BR>\n" );
document.write( "x - 3y + 4z = 6\r<BR>\n" );
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document.write( "I know that I could start by solving for x in the third equation:<BR>\n" );
document.write( "x = 3y - 4z +6\r<BR>\n" );
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document.write( "I can also solve for y in the first equation: y = 3 - x - z<BR>\n" );
document.write( "I could then substitute y in the second and third equation:<BR>\n" );
document.write( "x + 3 - x - z + z =  3   but this makes all variables 0<BR>\n" );
document.write( "x - 3(3 - x - z) + 4z = 6  x - 9 + 3x + 3z + 4z = 3   4x + 7z = 12\r<BR>\n" );
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document.write( "Now I'm stuck.  Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117400 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=117400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have a substitution problem that I would like help with, please (I have a test tomorrow). <BR>\n" );
document.write( "x + y + z = 3<BR>\n" );
document.write( "3x + 3y + 3z = 10<BR>\n" );
document.write( "x - 3y + 4z = 6 <BR>\n" );
document.write( "I know that I could start by solving for x in the third equation:<BR>\n" );
document.write( "x = 3y - 4z +6 <BR>\n" );
document.write( "I can also solve for y in the first equation: y = 3 - x - z<BR>\n" );
document.write( "I could then substitute y in the second and third equation:<BR>\n" );
document.write( "x + 3 - x - z + z = 3 but this makes all variables 0<BR>\n" );
document.write( "x - 3(3 - x - z) + 4z = 6 x - 9 + 3x + 3z + 4z = 3 4x + 7z = 12 <BR>\n" );
document.write( "Now I'm stuck. Thank you!<BR>\n" );
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document.write( "The best approach is to solve for one variable, then sub into the other 2 eqns.  The result will be 2 eqns in 2 variables.  Then sub for one of those.<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "x + y + z = 3<BR>\n" );
document.write( "3x + 3y + 3z = 10<BR>\n" );
document.write( "x - 3y + 4z = 6 <BR>\n" );
document.write( "I know that I could start by solving for x in the third equation:<BR>\n" );
document.write( "x = 3y - 4z +6<BR>\n" );
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document.write( "Now sub for x in the other 2 eqns<BR>\n" );
document.write( "x + y + z = 3<BR>\n" );
document.write( "3x + 3y + 3z = 10<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "3y-4z+6 + y + z = 3<BR>\n" );
document.write( "3(3y-4z+6) +3y +3z = 10<BR>\n" );
document.write( "Collect terms<BR>\n" );
document.write( "4y - 3z = -3<BR>\n" );
document.write( "12y -9z = -8<BR>\n" );
document.write( "Solve the 1st for y<BR>\n" );
document.write( "y = (-3+3z)/4<BR>\n" );
document.write( "Sub into the 2nd<BR>\n" );
document.write( "12((-3+3z))/4 - 9z = -8<BR>\n" );
document.write( "-9 + 9z - 9z = -8<BR>\n" );
document.write( "-9 = -8  This means there's no solution.<BR>\n" );
document.write( "If you look at the 1st and 2nd original eqns, all 3 variables in the 2nd are 3 times in the 1st, so there are actually 2 eqns (with an inconsistency) in 3 unknowns.  There is no one solution, there are an infinite number of solutions.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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