document.write( "Question 466669: I am really having a hard time with these 2 problems: Please help me!! :)
\n" ); document.write( "--Solve any way you can:\r
\n" ); document.write( "\n" ); document.write( "a) 2x-y+z=8
\n" ); document.write( " x+2y+z=-3
\n" ); document.write( " x-2y-z=7\r
\n" ); document.write( "\n" ); document.write( "b) 3x-y-2z=11
\n" ); document.write( " x-2y+3z=12
\n" ); document.write( " x+y-2z=5 \n" ); document.write( "

Algebra.Com's Answer #319960 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
I am really having a hard time with these 2 problems: Please help me!! :)
\n" ); document.write( "--Solve any way you can:
\n" ); document.write( "

\r\n" );
document.write( "a) 2x -  y + z =  8\r\n" );
document.write( "    x + 2y + z = -3\r\n" );
document.write( "    x - 2y - z =  7\r\n" );
document.write( "\r\n" );
document.write( "Add the 1st and 3rd equations and the z's\r\n" );
document.write( "will cancel out\r\n" );
document.write( "\r\n" );
document.write( "   2x -  y + z =  8\r\n" );
document.write( "    x - 2y - z =  7\r\n" );
document.write( " ------------------\r\n" );
document.write( "   3x - 3y     = 15\r\n" );
document.write( "\r\n" );
document.write( "And what's more, that can be divided through\r\n" );
document.write( "by 3\r\n" );
document.write( "\r\n" );
document.write( "        x - y  =  5\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next add the 2nd and 3rd equations and the z's\r\n" );
document.write( "will also cancel out\r\n" );
document.write( "\r\n" );
document.write( "     x + 2y + z = -3\r\n" );
document.write( "     x - 2y - z =  7\r\n" );
document.write( "   ------------------\r\n" );
document.write( "    2x          = 4\r\n" );
document.write( "              x = 2\r\n" );
document.write( "\r\n" );
document.write( "Substitute in \r\n" );
document.write( "\r\n" );
document.write( "        x - y = 5\r\n" );
document.write( "        2 - y = 5\r\n" );
document.write( "           -y = 3\r\n" );
document.write( "            y = -3  \r\n" );
document.write( "  \r\n" );
document.write( "Substitute in this original equation:\r\n" );
document.write( "\r\n" );
document.write( "    2x -  y + z = 8\r\n" );
document.write( "2(2) - (-3) + z = 8\r\n" );
document.write( "      4 + 3 + z = 8\r\n" );
document.write( "          7 + z = 8 \r\n" );
document.write( "              z = 1\r\n" );
document.write( "\r\n" );
document.write( "(x,y,z) = (2,-3,1)\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "b) 3x -  y - 2z = 11\r\n" );
document.write( "    x - 2y + 3z = 12\r\n" );
document.write( "    x +  y - 2z =  5\r\n" );
document.write( "\r\n" );
document.write( "Add the 1st and 3rd equations and the y's\r\n" );
document.write( "will cancel out\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   3x -  y - 2z = 11\r\n" );
document.write( "    x +  y - 2z =  5\r\n" );
document.write( "   -----------------\r\n" );
document.write( "   4x      - 4z = 16\r\n" );
document.write( "\r\n" );
document.write( "And what's more, that can be divided through\r\n" );
document.write( "by 4  (that rhymes)\r\n" );
document.write( "\r\n" );
document.write( "    x      -  z = 4\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To make the y's cancel in the 2nd and 3rd\r\n" );
document.write( "original equations which are:\r\n" );
document.write( "\r\n" );
document.write( "    x - 2y + 3z = 12\r\n" );
document.write( "    x +  y - 2z =  5\r\n" );
document.write( "\r\n" );
document.write( "we will have to multiply the bottom one through by 2 \r\n" );
document.write( "and add them:\r\n" );
document.write( "\r\n" );
document.write( "    x - 2y + 3z = 12\r\n" );
document.write( "   2x + 2y - 4z = 10\r\n" );
document.write( "  -------------------\r\n" );
document.write( "   3x      -  z = 22\r\n" );
document.write( "\r\n" );
document.write( "Now we have a system of two equations in two unknowns:\r\n" );
document.write( "\r\n" );
document.write( "    x - z =  4\r\n" );
document.write( "   3x - z = 22\r\n" );
document.write( "\r\n" );
document.write( "Multiply the 1st one through by -1 and the z's will cancel\r\n" );
document.write( "when you add them:\r\n" );
document.write( "\r\n" );
document.write( "   -x + z = -4\r\n" );
document.write( "   3x - z = 22\r\n" );
document.write( ":  -----------\r\n" );
document.write( "   2x     = 18\r\n" );
document.write( "        x = 9\r\n" );
document.write( "\r\n" );
document.write( "Substitute in\r\n" );
document.write( "\r\n" );
document.write( "    x - z = 4\r\n" );
document.write( "    9 - z = 4\r\n" );
document.write( "       -z = 4-9\r\n" );
document.write( "       -z = -5\r\n" );
document.write( "        z = 5\r\n" );
document.write( "\r\n" );
document.write( " Substitute in the original equation:\r\n" );
document.write( "\r\n" );
document.write( "    x +  y - 2z = 5\r\n" );
document.write( " (9) + y - 2(5) = 5\r\n" );
document.write( "     9 + y - 10 = 5\r\n" );
document.write( "          y - 1 = 5\r\n" );
document.write( "              y = 6\r\n" );
document.write( "\r\n" );
document.write( "(x,y,z) = (9,6,5)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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

\n" );