document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146538>Question 146538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system using any algebraic method.\r<BR>\n" );
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document.write( "1. \r<BR>\n" );
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document.write( "x-y+z=5<BR>\n" );
document.write( "2y+3z=14<BR>\n" );
document.write( "-3y+2z=5\r<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "2x+2y+z=-5<BR>\n" );
document.write( "2x+y+3z=7<BR>\n" );
document.write( "-4x-2y-6z=-14\r<BR>\n" );
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document.write( "Thank you so much! I'm really confused. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106986 by </B><A HREF=/tutors/aboutme.mpl?userid=aswathytony><B>aswathytony(47)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=aswathytony><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=106986\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a set of linear equation in x,y,z.<BR>\n" );
document.write( "1. x - y + z = 5     ..........(1)<BR>\n" );
document.write( "  2y + 3z = 14.............(2)<BR>\n" );
document.write( " -3y + 2z =5...............(3)\r<BR>\n" );
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document.write( "eq: (2 ) & (3) contains two variables y & z, make any one of the variable's coefficient same & eliminate.<BR>\n" );
document.write( "  (2) x 3 & (3) x 2, we get<BR>\n" );
document.write( "  2y x 3 + 3z x 3 = 14 x 3      ...........(4)<BR>\n" );
document.write( "  -3y x2 +2z x 2 = 5 x 2...................(5)\r<BR>\n" );
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document.write( "i.e. 6y +9z = 42 ........(4)<BR>\n" );
document.write( "    -6y + 4z = 10 .........(5)<BR>\n" );
document.write( "(4) +(5) ,when you add the like terms of this two eq: y term gets eliminated. i.e.  13z = 52 ; z = 52 / 13 = 4. now substitute z=4  in (2) & get the value of y.<BR>\n" );
document.write( "i.e 2y + 3 x 4 =14.<BR>\n" );
document.write( "  2y +12 = 14 <BR>\n" );
document.write( "  2y = 14 - 12 = 2;  y = 2/2 =1.<BR>\n" );
document.write( "substitute  z=4 &y=1 in eq: (1)<BR>\n" );
document.write( "  x - 1 +4 = 5<BR>\n" );
document.write( " x + 3 = 5 <BR>\n" );
document.write( "  x = 5-3 =2. <BR>\n" );
document.write( "the solution ; x= 2, y = 1 & z= 4.<BR>\n" );
document.write( "( you can cross check your answer by substituting all three values in any of the given eq: i.e. from (1)  x - y +z= 2 - 1 + 4 = 1 + 4 = 5 , so answer is correct)\r<BR>\n" );
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document.write( "2. 2x + 2y + z = -5.  .........(1)<BR>\n" );
document.write( "  2x + y + 3z = 7 .......(2)<BR>\n" );
document.write( "  -4x -2y -6z = -14. ...........(3)\r<BR>\n" );
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document.write( "solve (1) & (2), since coefficients of x are same by subtracting eliminate x<BR>\n" );
document.write( "  (1) - (2),<BR>\n" );
document.write( "y -2z = -12; y = -12 +2z ..........(4)<BR>\n" );
document.write( "now take eq: (1)& (3), coefficients of y are same, eliminate y<BR>\n" );
document.write( "    - 2x -5z = -19<BR>\n" );
document.write( "       -2x = -19 + 5z<BR>\n" );
document.write( "     x= 19- 5z/2  .........(5)substituting (4) & (5) in (1) & solve<BR>\n" );
document.write( "  2x + 2y + z = -5<BR>\n" );
document.write( "  2 ( 19- 5z/2) + 2 ( -12 +2z) + z = -5.<BR>\n" );
document.write( "   19 - 5z  - 24 +4z +z = -5.<BR>\n" );
document.write( "  -5z +4z +z + 19 -24 = -5<BR>\n" );
document.write( "       -5z+ 5z - 5 = -5<BR>\n" );
document.write( "    0= 0. , this shows that the equations has infinite solutions.<BR>\n" );
document.write( "here eq: (2) & (3) are one and same line .( multiply (2) with -2 , we get eq: (3), i.e. these two equations are same).  such  linear equations has infinite solutions.<BR>\n" );
document.write( "( before solving system of equation , verify whether given lines are same, if not then proceed for solution. above steps are for clearing doubts, no need to do it if lines are same) \r<BR>\n" );
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document.write( " </SPAN>\n" );
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