document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=14103>Question 14103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x+3y+4z=2<BR>\n" );
document.write( "5x-2y+3z=0<BR>\n" );
document.write( "x-5y-2z=-4\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 #7373 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=7373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE THE FOLLOWING SOLUTION GIVEN BY ME TO A SIMILAR PROBLEM AND WORK THE SOLUTION YOUR SELF.<BR>\n" );
document.write( "Answer 7295 by venugopalramana(11)   on 2005-10-10 05:14:13 (Show Source): \r<BR>\n" );
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document.write( "Hi Tutors:<BR>\n" );
document.write( "I have working on this problem for some time but I am still having a hard time working this one:<BR>\n" );
document.write( "I am suppose to solve this system using elimination method<BR>\n" );
document.write( "10x+6y+z=7 (1)<BR>\n" );
document.write( "5x-9y-2z=3 (2)<BR>\n" );
document.write( "15x-12y+2z=-5 (3) <BR>\n" );
document.write( "20x-21y=-2 (4) <BR>\n" );
document.write( "Please show me how to work this problem from this point.<BR>\n" );
document.write( "Thank you <BR>\n" );
document.write( "Good you have proceeded correctly and infact on the way to solving the problem by your self..you only need a little guidance on the path you should follow to solve the problem..o.k. ..let us see you have added equations 2 and 3 to get equation 3 ,which has accomplished elimination of one unknown z . The basic procedure is , if we start with 3 equations in 3 unknowns ,we try to eliminate one unknown taking one pair of equations at a time to get 2 new equations in 2 unknowns only.Then we take those 2 new equations to eliminate one another unknown to get one more new equation , but this time with one unknown only.This we can easily solve to find the unknown.Now , we travel backwards along the same path as we travelled to find the 2 other unknowns one after another by substituting the known values every time.Let us illustrate the procedure now with this example.Now that you have already got one new equation 4 from 2 and 3 to eliminate z., let us take equations 1 and 2 to eliminate the same unknown z.For this we observe the coefficients of z in the two equations which are 1 and -2 respectively.So we multiply equation 1 with 2 and add it to equation 2.<BR>\n" );
document.write( "Eqn.1 * 2 gives us ...20x+12y+2z=14 .....(5)<BR>\n" );
document.write( "Eqn.2 is .............5x-9y-2z = 3........(6)<BR>\n" );
document.write( "Eqn.5 + Eqn.6 gives us .....25x+3y = 17....(7)<BR>\n" );
document.write( "but from Eqn.4 we have .....20x-21y=-2......(4)..proceeding on the same basis ,we eliminate y from these 2 equations.<BR>\n" );
document.write( "Eqn.7 * 7 gives us .........175x+21y=119....(8)<BR>\n" );
document.write( "Eqn.8 + Eqn.4 gives us .....195x=117 ..or x= 117/195 = 39/65 = 3/5.....now substitute this value of x in eqn.4 to get y<BR>\n" );
document.write( "y=(20*(3/5)+2)/21=14/21=2/3…….now substitute these values of x and y in eqn.1 to get z.<BR>\n" );
document.write( "z=(7-10*(3/5)-6*(2/3))=-3………….. As a check ,you can substitute these values of x,y,and z in the 3 given equations to <BR>\n" );
document.write( "verify that your answer is correct.\r<BR>\n" );
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