document.write( "Question 1002469: 3x+2y-8z=29
\n" ); document.write( "9x-y+2z=23
\n" ); document.write( "-x-2y+8z=-11 \n" ); document.write( "

Algebra.Com's Answer #853937 by n2(78) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "3x + 2y - 8z = 29
\n" ); document.write( "9x - y + 2z = 23
\n" ); document.write( "-x - 2y + 8z = -11
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "So, your original system of equation is\r\n" );
document.write( "\r\n" );
document.write( "    3x + 2y - 8z =  29    (1)\r\n" );
document.write( "    9x -  y + 2z =  23    (2)\r\n" );
document.write( "    -x - 2y + 8z = -11    (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Add equations (1) and (3).  The terms with 'y' and 'z' will cancel each other, and you will get then\r\n" );
document.write( "\r\n" );
document.write( "    3x - x = 29 - 11,  --->  2x = 18,  --->  x = 18/2 = 9.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now substitute this value x = 9 into the first and second equations\r\n" );
document.write( "\r\n" );
document.write( "    3*9 + 2y - 8z = 29     (1')\r\n" );
document.write( "    9*9 -  y + 2z = 23     (2')\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify\r\n" );
document.write( "\r\n" );
document.write( "          2y - 8z =   2    (1'')\r\n" );
document.write( "          -y + 2z = -58    (2'')\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we are on the straight finish line: we only need to solve one 2x2-syatem of equations (1''), (2'').\r\n" );
document.write( "\r\n" );
document.write( "Solve it by the Elimination method. For it, multiply equation (2'') by 2 (both sides) and add to equation (1'').\r\n" );
document.write( "You will get\r\n" );
document.write( "\r\n" );
document.write( "             - 8z + 4z = 2 + 2*(-58),  --->  -4z = -114,  z = (-114)/(-4) = 28.5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now from equation (2'')\r\n" );
document.write( "\r\n" );
document.write( "           y = 58 + 2*28.5 = 115.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The solution to the given system is x= 9,  y = 115,  z = 28.5.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );