document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189199>Question 189199</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each of these system of equations. \r<BR>\n" );
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document.write( "1) x + 2y + z = 10\r<BR>\n" );
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document.write( "   2x - y + 3z = -5\r<BR>\n" );
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document.write( "   2x - 3y - 5z = 27<BR>\n" );
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document.write( "a) x = 4, y = 7, z = -5<BR>\n" );
document.write( "b) x = -5, y = 4, z =7<BR>\n" );
document.write( "c) x = 7, y = -5, z = 4<BR>\n" );
document.write( "d) x = 7, y = 4, z = -5 \r<BR>\n" );
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document.write( "On this question use the RREF function on your calculator\r<BR>\n" );
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document.write( "2)  3x + y + z = 4\r<BR>\n" );
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document.write( "    2x + 2y + 3z = 3\r<BR>\n" );
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document.write( "    x + 3y + 2z = 5<BR>\n" );
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document.write( "a) x = -1, y = 2, z = 1<BR>\n" );
document.write( "b) x = 2, y = 1, z = -1<BR>\n" );
document.write( "c) x = 1, y = 2, z = -1<BR>\n" );
document.write( "d) x = 1, y = -1, z = 2 \r<BR>\n" );
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document.write( "May you explain how to solve these questions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141935 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=141935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve each of these system of equations. <BR>\n" );
document.write( "1) x + 2y + z = 10 <BR>\n" );
document.write( "2x - y + 3z = -5 <BR>\n" );
document.write( "2x - 3y - 5z = 27\r<BR>\n" );
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document.write( "a) x = 4, y = 7, z = -5<BR>\n" );
document.write( "b) x = -5, y = 4, z =7<BR>\n" );
document.write( "c) x = 7, y = -5, z = 4<BR>\n" );
document.write( "d) x = 7, y = 4, z = -5 <BR>\n" );
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document.write( " x + 2y + z = 10 <BR>\n" );
document.write( "2x - y + 3z = -5 <BR>\n" );
document.write( "2x - 3y - 5z = 27<BR>\n" );
document.write( "There's more than one way to do these.  If you get one on a timed test, and you have 4 solutions to choose from, as in this one, sub the values in to find which of the 4 it is.  That's quicker by far, IF you don't have to show your work for the test.<BR>\n" );
document.write( "Then there's elimination and substitution.  You pick one of the 3 variables and eliminate it from 2 of the equations.  x is as good as any for this problem.<BR>\n" );
document.write( "Multiply by whatever is needed to get the same coeffs for all 3 eqns, in this case eqn 1 times 2 will do it.\r<BR>\n" );
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document.write( " x + 2y + z = 10 --><BR>\n" );
document.write( "2x + 4y + 2z = 20<BR>\n" );
document.write( "2x - y + 3z = -5 <BR>\n" );
document.write( "2x - 3y - 5z = 27<BR>\n" );
document.write( "Then subtract one eqn, the 3rd, from the 1st and the 2nd.<BR>\n" );
document.write( "2x + 4y + 2z = 20<BR>\n" );
document.write( "2x - 3y - 5z = 27<BR>\n" );
document.write( "----------------- Subtract<BR>\n" );
document.write( "0x + 7y + 7z = -7  eqn A<BR>\n" );
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document.write( "2x - y + 3z = -5 <BR>\n" );
document.write( "2x - 3y - 5z = 27<BR>\n" );
document.write( "----------------- Subtract<BR>\n" );
document.write( "0x + 2y + 8z = -32 eqn B<BR>\n" );
document.write( "Now there are 2 eqns in 2 variables, A and B.<BR>\n" );
document.write( "Multiply again to get the same coeffs<BR>\n" );
document.write( "y + z = -1<BR>\n" );
document.write( "y + 4z = -16<BR>\n" );
document.write( "------------ Subtract<BR>\n" );
document.write( "0y -3z = 15<BR>\n" );
document.write( "z = -5 zzzzzzzzzzzzzzzzzzzzzzzzzzzz<BR>\n" );
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document.write( "y + z = -1<BR>\n" );
document.write( "y = 4 yyyyyyyyyyyyyyyyyyyyyyyyyyyyyy<BR>\n" );
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document.write( "x + 2y + z = 10<BR>\n" );
document.write( "x = 7 xxxxxxxxxxxxxxxxxxxxxxxxxxxx<BR>\n" );
document.write( "That's answer d.<BR>\n" );
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document.write( "Another method is determinants.  I made an Excel sheet that does these up to 4 by 4.<BR>\n" );
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document.write( "I don't have a calculator that does these.<BR>\n" );
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