document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=660956>Question 660956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this system of equations:\r<BR>\n" );
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document.write( "Directions: Solve using elimination and using the matrix method<BR>\n" );
document.write( "x+y+z=6<BR>\n" );
document.write( "2x-3y+5z=-11<BR>\n" );
document.write( "x+3y-4z=19\r<BR>\n" );
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document.write( "Work I have done so far:\r<BR>\n" );
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document.write( "x+y+z=6<BR>\n" );
document.write( "-x-3y+4z=-19              This equals -2y+5z=-13     equation #1\r<BR>\n" );
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document.write( "-2x-6y+8z=-38<BR>\n" );
document.write( "2x-3y+5z=-11              This equals -9y+13z=-49    equation #2\r<BR>\n" );
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document.write( "Multiply equation #1 by -9 and multiply equation #2 by 2\r<BR>\n" );
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document.write( "18y+45z=117<BR>\n" );
document.write( "-18y-26z=-98             z= -19/71\r<BR>\n" );
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document.write( "At this point I got stuck because my teacher said that all answers would be nice even numbers.  When I solved the equations using the matrix method (I know how to do this part) I got (3,4,-1) which I checked and is the correct answer.\r<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 #411440 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=411440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Please help me solve this system of equations:\r<BR>\n" );
document.write( "\n" );
document.write( "Directions: Solve using elimination and using the matrix method<BR>\n" );
document.write( "x+y+z=6<BR>\n" );
document.write( "2x-3y+5z=-11<BR>\n" );
document.write( "x+3y-4z=19\r<BR>\n" );
document.write( "\n" );
document.write( "Work I have done so far:\r<BR>\n" );
document.write( "\n" );
document.write( "x+y+z=6<BR>\n" );
document.write( "-x-3y+4z=-19              This equals -2y+5z=-13     equation #1\r<BR>\n" );
document.write( "\n" );
document.write( "-2x-6y+8z=-38<BR>\n" );
document.write( "2x-3y+5z=-11              This equals -9y+13z=-49    equation #2\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply equation #1 by -9 and multiply equation #2 by 2\r<BR>\n" );
document.write( "\n" );
document.write( "18y+45z=117<BR>\n" );
document.write( "-18y-26z=-98             z= -19/71\r<BR>\n" );
document.write( "\n" );
document.write( "At this point I got stuck because my teacher said that all answers would be nice even numbers.  When I solved the equations using the matrix method (I know how to do this part) I got (3,4,-1) which I checked and is the correct answer.\r<BR>\n" );
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document.write( "It would seem as though you multiplied - 9y + 13z = - 49 by 2, which results in: - 18y + 26z = - 98, NOT - 18y - 26z = - 98. This is where you went wrong. Look into this and you should be fine. My elimination-solution is below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system+%28x+%2B+y+%2B+z+=+6_______eq+%28i%29%2C%0D%0A2x+-+3y+%2B+5z+=+-+11______eq+%28ii%29%2C%0D%0Ax+%2B+3y+-+4z+=+19______eq+%28iii%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- 2x – 2y – 2z = - 12 ------- Multiplying eq (i) by – 2 ------ eq (iv)\r<BR>\n" );
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document.write( "– 5y + 3z = - 23 ------- Adding eqs (iv) and (ii) ----- eq (v)<BR>\n" );
document.write( "- 2y + 5z = - 13 ------- Subtract eq (iii) from eq (i) ----- eq (vi)\r<BR>\n" );
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document.write( "10y – 6z = 46 ------- Multiplying eq (v) by – 2 ------ eq (vii)<BR>\n" );
document.write( "- 10y + 25z = - 65 ------- Multiplying eq (vi) by 5 ------ eq (viii)<BR>\n" );
document.write( "19z = - 19 -------- Adding eqs (viii) & (vii)<BR>\n" );
document.write( "z = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-+19%29%2F19 ALIGN=MIDDLE  ALT=\"%28-+19%29%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28z+=+-+1%29 ALIGN=MIDDLE  ALT=\"highlight_green%28z+=+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "– 5y + 3(- 1) = - 23 ------- Substituting – 1 for z in eq (v) <BR>\n" );
document.write( "- 5y – 3 = - 23 <BR>\n" );
document.write( "– 5y = - 23 + 3 <BR>\n" );
document.write( "– 5y = - 20<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-+20%29%2F-+5 ALIGN=MIDDLE  ALT=\"%28-+20%29%2F-+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y+=+4%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y+=+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x + 4 - 1 = 6 ----- Substituting 4 for y and – 1 for z in eq (i)<BR>\n" );
document.write( "x + 3 = 6<BR>\n" );
document.write( "x = 6 - 3, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x+=+3%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x+=+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at MathMadEzy@aol.com  </SPAN>\n" );
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