document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208209>Question 208209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SYSTEM OF 3 EQUATIONS WITH 3 UNKNOWNS<BR>\n" );
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document.write( "FIND SOLUTION SET FOR THE FOLLOWING SYSTEM OF EQUATIONS:\r<BR>\n" );
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document.write( " X  -Y  +5Z =  2<BR>\n" );
document.write( " 4X -3Y +5Z =  3<BR>\n" );
document.write( " 3X -2Y +4Z =  1<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157518 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 3 equations in 3 unknowns.<BR>\n" );
document.write( "you want to reduce that to 2 equations in 2 unknowns<BR>\n" );
document.write( "you then reduce that to 1 equation in one unknown<BR>\n" );
document.write( "working your way back up the chain...<BR>\n" );
document.write( "you then solve for the first unknown<BR>\n" );
document.write( "you then solve for the second unknown<BR>\n" );
document.write( "you then solve for the third unknown.<BR>\n" );
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document.write( "your equations are:<BR>\n" );
document.write( "x - y + 5z = 2 = equation 1<BR>\n" );
document.write( "4x - 3y + 5z = 3 = equation 2<BR>\n" );
document.write( "3x - 2y + 4z = 1 = equation 3<BR>\n" );
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document.write( "you can eliminate z first.<BR>\n" );
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document.write( "you subtract equation 1 from equation 2 to get:<BR>\n" );
document.write( "3x - 2y = 1 = equation 4<BR>\n" );
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document.write( "you multiply equation 1 by 4 to get:<BR>\n" );
document.write( "4x - 4y + 20z = 8 = equation 5<BR>\n" );
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document.write( "you multiply equation 3 by 5 to get:<BR>\n" );
document.write( "15x - 10y + 20z = 5 = equation 6<BR>\n" );
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document.write( "you subtract equation 5 from equation 6 to get:<BR>\n" );
document.write( "11x - 6y = -3 = equation 7<BR>\n" );
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document.write( "you now have 2 equations in 2 unknowns.<BR>\n" );
document.write( "those are equation 4 and equation 7 shown below:<BR>\n" );
document.write( "3x - 2y = 1 = equation 4<BR>\n" );
document.write( "11x - 6y = -3 = equation 7<BR>\n" );
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document.write( "next you will eliminate the y to get one equation in one unknown.,<BR>\n" );
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document.write( "you multiply equation 4 by 3 to get:<BR>\n" );
document.write( "9x - 6y = 3 = equation 8<BR>\n" );
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document.write( "you subtract equation 8 from equation 7 to get:<BR>\n" );
document.write( "2x = -6<BR>\n" );
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document.write( "you now have one equation in one unknown which you solve to get:<BR>\n" );
document.write( "x = -3<BR>\n" );
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document.write( "you now go back to equation 4 or equation 7 and solve for y.<BR>\n" );
document.write( "let's use equation 7<BR>\n" );
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document.write( "11x - 6y = -3 = equation 7<BR>\n" );
document.write( "replace x with -3 to get:<BR>\n" );
document.write( "11 *(-3) - 6y = -3<BR>\n" );
document.write( "-33 - 6y = -3<BR>\n" );
document.write( "6y = -30<BR>\n" );
document.write( "y = -5<BR>\n" );
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document.write( "you now have:<BR>\n" );
document.write( "x = -3<BR>\n" );
document.write( "y = -5<BR>\n" );
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document.write( "go back to equation 1 or 2 or 3 and replace x with -3 and replace y with -5 to solve for z.<BR>\n" );
document.write( "we'll use equation 2 as shown below:<BR>\n" );
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document.write( "4x - 3y + 5z = 3 = equation 2<BR>\n" );
document.write( "replace x with -3 and y with -5 to get:<BR>\n" );
document.write( "4 * (-3) - 3 * (-5) + 5z = 3<BR>\n" );
document.write( "-12 + 15 + 5z = 3<BR>\n" );
document.write( "3 + 5z = 3<BR>\n" );
document.write( "5z = 0<BR>\n" );
document.write( "z = 0<BR>\n" );
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document.write( "you now have:<BR>\n" );
document.write( "x = -3<BR>\n" );
document.write( "y = -5<BR>\n" );
document.write( "z = 0<BR>\n" );
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document.write( "your equation should be solved and you confirm that by replacing x with -3 and y with -5 and z with 0 in all 3 of your equations to make sure that the equations are true with those values in them for x,y,z.<BR>\n" );
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document.write( "your original equations are:<BR>\n" );
document.write( "x - y + 5z = 2 = equation 1<BR>\n" );
document.write( "4x - 3y + 5z = 3 = equation 2<BR>\n" );
document.write( "3x - 2y + 4z = 1 = equation 3<BR>\n" );
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document.write( "equation 1 becomes -3 + 5 + 0 = 2 which becomes 2 = 2 which is true.<BR>\n" );
document.write( "equation 2 becomes -12 + 15 + 0 = 3 which becomes 3 = 3 which is true.<BR>\n" );
document.write( "equation 3 becomes -9 + 10 + 0 = 1 which becomes 1 = 3 which is true.<BR>\n" );
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document.write( "all 3 equations are true so the values for x,y,z satisfy all of them simultaneously and you are done.<BR>\n" );
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