document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=45903>Question 45903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the system of equations\r<BR>\n" );
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document.write( "3x-4y=-3<BR>\n" );
document.write( "6x+2z=-7/2<BR>\n" );
document.write( "2y-4z=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #30510 by </B><A HREF=/tutors/aboutme.mpl?userid=abhijitvakil><B>abhijitvakil(7)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=abhijitvakil><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=30510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets day the equations are numbered 1, 2 & 3 as under\r<BR>\n" );
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document.write( "3x - 4y = -3  ....... 1<BR>\n" );
document.write( "6x + 2z = -7/2 ...... 2<BR>\n" );
document.write( "2y - 4z =  4   ...... 3\r<BR>\n" );
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document.write( "The approach is to use one equation to express the value of one of the variables in terms of the other, and then use this value in another equation, as a result of which we get 2 equations in 2 variables, which can then be easily solved. Note -\r<BR>\n" );
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document.write( "Eq 3 is divided by 2 to give :\r<BR>\n" );
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document.write( "y - 2z = 2 ;\r<BR>\n" );
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document.write( "So we may write\r<BR>\n" );
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document.write( "y = 2 - 2z ....  4\r<BR>\n" );
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document.write( "Use this value of y in eq 1 above, we get\r<BR>\n" );
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document.write( "3x - 4(2-2z) = -3\r<BR>\n" );
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document.write( "or \r<BR>\n" );
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document.write( "3x - 8 + 8z = -3<BR>\n" );
document.write( "or\r<BR>\n" );
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document.write( "3x + 8z = 5 ...... eq no 5\r<BR>\n" );
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document.write( "Multiply this equation by 2, we get\r<BR>\n" );
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document.write( "6x + 16z = 10 .... eq no 6\r<BR>\n" );
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document.write( "Subtract eq no 2 from eq no 6, we get\r<BR>\n" );
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document.write( "6x + 16z - 6x - 2z = 10 + 7/2<BR>\n" );
document.write( "or<BR>\n" );
document.write( "14z = 10 + 7/2<BR>\n" );
document.write( "or <BR>\n" );
document.write( "z = 10/14 + 7/(2*14)\r<BR>\n" );
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document.write( "or <BR>\n" );
document.write( "z = 5/7 + 1/4 =27/28. \r<BR>\n" );
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document.write( "Use this value of z in eq 2 to get the value of x & eq 3 to get the value of y. </SPAN>\n" );
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