document.write( "Question 93732: Solve each of the following systems by addition.
\n" ); document.write( "2x+3y=1
\n" ); document.write( "5x+3y=16 \n" ); document.write( "
Algebra.Com's Answer #68289 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Solve each of the following systems by addition.\r\n" );
document.write( "2x+3y =  1\r\n" );
document.write( "5x+3y = 16\r\n" );
document.write( "\r\n" );
document.write( "The idea is to multiply each equation by whatever number\r\n" );
document.write( "will be such that when you add the equations vertically,\r\n" );
document.write( "one of the letters will cancel out.  The 3y in the top can be\r\n" );
document.write( "made to cancel with the 3y in the bottom if one of them\r\n" );
document.write( "became -3y and the other remained +3y.  So we multiply the\r\n" );
document.write( "first equation through by -1 and the second equation through\r\n" );
document.write( "by +1:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-1[2x+3y =  1]\r\n" );
document.write( "+1[5x+3y = 16]\r\n" );
document.write( "\r\n" );
document.write( "This becomes:\r\n" );
document.write( "\r\n" );
document.write( "  -2x-3y = -1\r\n" );
document.write( "   5x+3y = 16\r\n" );
document.write( "\r\n" );
document.write( "Now we draw a line underneath and add\r\n" );
document.write( "vertically term by term:\r\n" );
document.write( "\r\n" );
document.write( "  -2x-3y = -1\r\n" );
document.write( "   5x+3y = 16\r\n" );
document.write( "   ----------\r\n" );
document.write( "   3x    = 15\r\n" );
document.write( "\r\n" );
document.write( "Which we solve and get\r\n" );
document.write( "\r\n" );
document.write( "       x = 5\r\n" );
document.write( "\r\n" );
document.write( "Now you can finish by switching over to\r\n" );
document.write( "substition, which is what many teachers\r\n" );
document.write( "and books tell you to do.  However, to \r\n" );
document.write( "finish by addition, start over and \r\n" );
document.write( "eliminate the x terms:\r\n" );
document.write( "\r\n" );
document.write( "2x+3y =  1\r\n" );
document.write( "5x+3y = 16\r\n" );
document.write( "\r\n" );
document.write( "The 2x in the top can be made to cancel with the 5x in the \r\n" );
document.write( "bottom if one of them becomes -10x and the other becomes\r\n" );
document.write( "+10x, since 10 is the LCM of 2 and 5.  So we multiply the \r\n" );
document.write( "first equation through by -5 and the second equation through \r\n" );
document.write( "by +2:\r\n" );
document.write( "\r\n" );
document.write( "-5[2x+3y =  1]\r\n" );
document.write( "+2[5x+3y = 16]\r\n" );
document.write( "\r\n" );
document.write( "This becomes:\r\n" );
document.write( "\r\n" );
document.write( " -10x-15y = -5\r\n" );
document.write( "  10x+ 6y = 32\r\n" );
document.write( "\r\n" );
document.write( "Now we draw a line underneath and add\r\n" );
document.write( "vertically term by term:\r\n" );
document.write( "\r\n" );
document.write( " -10x-15y = -5\r\n" );
document.write( "  10x+ 6y = 32\r\n" );
document.write( "   -----------\r\n" );
document.write( "      -9y = 27\r\n" );
document.write( "\r\n" );
document.write( "Which we solve and get\r\n" );
document.write( "\r\n" );
document.write( "        y = -3\r\n" );
document.write( "\r\n" );
document.write( "So the solution is \r\n" );
document.write( "\r\n" );
document.write( "(x,y) = (5,-3)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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