document.write( "Question 84763This question is from textbook finite mathmatics
\n" ); document.write( ": Select the point which is in the feasible region
\n" ); document.write( "of the system of inequalities. \r
\n" ); document.write( "\n" ); document.write( "2x + 3y < 8
\n" ); document.write( "5x + 2y < 7
\n" ); document.write( "x > 0, y > 0 \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "A. (1,2)
\n" ); document.write( "B. (1,1)
\n" ); document.write( "C. (0,3)
\n" ); document.write( "D. (3,2) \n" ); document.write( "
Algebra.Com's Answer #61060 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Select the point which is in the feasible region\r\n" );
document.write( "of the system of inequalities. \r\n" );
document.write( "\r\n" );
document.write( "2x + 3y < 8\r\n" );
document.write( "5x + 2y < 7\r\n" );
document.write( "x > 0, y > 0 \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "A. (1,2)\r\n" );
document.write( "B. (1,1)\r\n" );
document.write( "C. (0,3)\r\n" );
document.write( "D. (3,2)\r\n" );
document.write( "\r\n" );
document.write( "Substitute each of these points in each of the inequalities\r\n" );
document.write( "to fnd out which one(s) satisies them all:\r\n" );
document.write( "\r\n" );
document.write( "Try A:\r\n" );
document.write( "Substituting (x,y) = (1,2) in the first inequality:\r\n" );
document.write( "\r\n" );
document.write( "2x + 3y < 8\r\n" );
document.write( "\r\n" );
document.write( "2(1) + 3(2) < 8\r\n" );
document.write( "     2 + 6 < 8\r\n" );
document.write( "         8 < 8\r\n" );
document.write( "That is true.  So we substitute it in the second inequality:\r\n" );
document.write( "\r\n" );
document.write( "5x + 2y < 7\r\n" );
document.write( "5(1) + 2(2) < 7\r\n" );
document.write( " 5 + 4 < 7\r\n" );
document.write( "     9 < 7\r\n" );
document.write( "\r\n" );
document.write( "That is false, so we know (1,2) is not in the feasible region,\r\n" );
document.write( "and (A) is not a correct choice.\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Try B:\r\n" );
document.write( "Substituting (x,y) = (1,1) in the first inequality:\r\n" );
document.write( "\r\n" );
document.write( "2x + 3y < 8\r\n" );
document.write( "\r\n" );
document.write( "2(1) + 3(1) < 8\r\n" );
document.write( "     2 + 3 < 8\r\n" );
document.write( "         5 < 8\r\n" );
document.write( "That is true.  So we substitute it in the second inequality:\r\n" );
document.write( "\r\n" );
document.write( "5x + 2y < 7\r\n" );
document.write( "5(1) + 2(1) < 7\r\n" );
document.write( " 5 + 2 < 7\r\n" );
document.write( "     7 < 7\r\n" );
document.write( "\r\n" );
document.write( "That is also true. So we substitute it in the third inequality:\r\n" );
document.write( "\r\n" );
document.write( "x > 0\r\n" );
document.write( "\r\n" );
document.write( "1 > 0\r\n" );
document.write( "\r\n" );
document.write( "That is also true. So we substitute it in the fourth inequality:\r\n" );
document.write( "\r\n" );
document.write( "y > 0\r\n" );
document.write( "\r\n" );
document.write( "1 > 0\r\n" );
document.write( "\r\n" );
document.write( "That is also true, so (1,1) is in the feasible region. So\r\n" );
document.write( "(B) is a correct choice.\r\n" );
document.write( "\r\n" );
document.write( "------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Let's see if it could be either of the other two:\r\n" );
document.write( "\r\n" );
document.write( "Try C:\r\n" );
document.write( "Substituting (x,y) = (0,3) in the first inequality:\r\n" );
document.write( "\r\n" );
document.write( "2x + 3y < 8\r\n" );
document.write( "\r\n" );
document.write( "2(0) + 3(3) < 8\r\n" );
document.write( "     0 + 9 < 8\r\n" );
document.write( "         9 < 8\r\n" );
document.write( "\r\n" );
document.write( "That is false.  So we have eliminated C.\r\n" );
document.write( "\r\n" );
document.write( "---------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Try D:\r\n" );
document.write( "Substituting (x,y) = (3,2) in the first inequality:\r\n" );
document.write( "\r\n" );
document.write( "2x + 3y < 8\r\n" );
document.write( "\r\n" );
document.write( "2(3) + 3(2) < 8\r\n" );
document.write( "     6 + 6 < 8\r\n" );
document.write( "        12 < 8\r\n" );
document.write( "\r\n" );
document.write( "That is false.  So we have eliminated D.\r\n" );
document.write( "\r\n" );
document.write( "So the only correct choice is (B).\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );