document.write( "Question 662393: solve the following systems of linear equation in three variables by elimination or substitution.
\n" ); document.write( "1. x+y+z=6
\n" ); document.write( " 2x-y+3z=9
\n" ); document.write( " -x+2y+2z=9 \n" ); document.write( "
Algebra.Com's Answer #412201 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "1)      x +  y +  z = 6\r\n" );
document.write( "2)     2x -  y + 3z = 9\r\n" );
document.write( "3)     -x + 2y + 2z = 9\r\n" );
document.write( "\r\n" );
document.write( "Pick a letter to eliminate and a pair of equations that contain\r\n" );
document.write( "it and eliminate it from them:\r\n" );
document.write( "\r\n" );
document.write( "I choose to eliminate x from 1) and 3):\r\n" );
document.write( "\r\n" );
document.write( "1)      x +  y +  z =  6\r\n" );
document.write( "3)     -x + 2y + 2z =  9  Just add them term by term\r\n" );
document.write( "------------------------\r\n" );
document.write( "            3y + 3z = 15  Divide thru by 3\r\n" );
document.write( "4)           y +  z =  5\r\n" );
document.write( "\r\n" );
document.write( "Pick one of the equations that you just used along\r\n" );
document.write( "with the equation you haven't used and eliminate the\r\n" );
document.write( "SAME letter you just eliminated. \r\n" );
document.write( "\r\n" );
document.write( "I pick 1) and 2) to eliminate x from:\r\n" );
document.write( "\r\n" );
document.write( "1)      x +  y +  z = 6\r\n" );
document.write( "2)     2x -  y + 3z = 9 \r\n" );
document.write( "----------------------- Multiply 10 thru by -2\r\n" );
document.write( "\r\n" );
document.write( "      -2x - 2y - 2z = -12\r\n" );
document.write( "2)     2x -  y + 3z =   9 \r\n" );
document.write( "-------------------------\r\n" );
document.write( "5)         -3y +  z =  -3\r\n" );
document.write( "\r\n" );
document.write( "Solve the resulting 2x2 system of equations:\r\n" );
document.write( "\r\n" );
document.write( "Now we take 4) and 5)\r\n" );
document.write( "\r\n" );
document.write( "4)           y +  z =  5\r\n" );
document.write( "5)         -3y +  z = -3\r\n" );
document.write( "\r\n" );
document.write( "Eliminate z by multiplying 4) by -1\r\n" );
document.write( "\r\n" );
document.write( "            -y -  z = -5\r\n" );
document.write( "5)         -3y +  z = -3\r\n" );
document.write( "------------------------\r\n" );
document.write( "6)         -4y      = -8\r\n" );
document.write( "                  y =  2\r\n" );
document.write( "\r\n" );
document.write( "Substitute in 4)\r\n" );
document.write( "\r\n" );
document.write( "4)            y + z = 5\r\n" );
document.write( "              2 + z = 5\r\n" );
document.write( "                  z = 3\r\n" );
document.write( "\r\n" );
document.write( " Substitute y = 2 and z = 3 in 1)\r\n" );
document.write( "\r\n" );
document.write( "1)        x + y + z = 6\r\n" );
document.write( "          x + 2 + 3 = 6\r\n" );
document.write( "              x + 5 = 6\r\n" );
document.write( "                  x = 1\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );