document.write( "Question 121307This question is from textbook algebra2 explorations and applications
\n" ); document.write( ": state weather the system has one solution, infinitely many solutions, or no solution.
\n" ); document.write( "3x+7y=2
\n" ); document.write( "6x+14y=4
\n" ); document.write( "
\n" ); document.write( "4x+5y=3
\n" ); document.write( "6x+9y=9\r
\n" ); document.write( "\n" ); document.write( "6x+11y=12
\n" ); document.write( "12x+22y=10\r
\n" ); document.write( "\n" ); document.write( "0.3x+0.7y=1.2
\n" ); document.write( "6x+14y=24 \n" ); document.write( "
Algebra.Com's Answer #89045 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "state whether the system has one solution, \r\n" );
document.write( "infinitely many solutions, or no solution. \r\n" );
document.write( "\r\n" );
document.write( "3x +  7y = 2 \r\n" );
document.write( "6x + 14y = 4 \r\n" );
document.write( "\r\n" );
document.write( " 4x + 5y = 3\r\n" );
document.write( " 6x + 9y = 9 \r\n" );
document.write( "\r\n" );
document.write( " 6x + 11y = 12\r\n" );
document.write( "12x + 22y = 10 \r\n" );
document.write( "\r\n" );
document.write( "0.3x + 0.7y = 1.2\r\n" );
document.write( "  6x +  14y =  24\r\n" );
document.write( "\r\n" );
document.write( "Rule:\r\n" );
document.write( "\r\n" );
document.write( "Ax + By = C\r\n" );
document.write( "Dx + Ey = F\r\n" );
document.write( "\r\n" );
document.write( "Calculate AE and BD\r\n" );
document.write( "\r\n" );
document.write( "case 1. AE ¹ BD. \r\n" );
document.write( "\r\n" );
document.write( "        Then there is exactly one solution.\r\n" );
document.write( "\r\n" );
document.write( "case 2. AE = BD.  Then calculate AF and CD.\r\n" );
document.write( "\r\n" );
document.write( "        If AF = CD then there are infinitely \r\n" );
document.write( "        many solutions.\r\n" );
document.write( "        If AF ¹ CD then there \r\n" );
document.write( "        are no solutions.\r\n" );
document.write( "\r\n" );
document.write( "---------------------------------\r\n" );
document.write( "---------------------------------\r\n" );
document.write( "\r\n" );
document.write( "3x +  7y = 2 \r\n" );
document.write( "6x + 14y = 4       \r\n" );
document.write( "\r\n" );
document.write( "A = 3, B = 7, C = 6, D = 6, E = 14, F = 4 \r\n" );
document.write( "\r\n" );
document.write( "Calculate AE and BD.  \r\n" );
document.write( "\r\n" );
document.write( "AE = (3)(14) = 42\r\n" );
document.write( "BD - (7)(6) = 42\r\n" );
document.write( "\r\n" );
document.write( "This is case 2:\r\n" );
document.write( "\r\n" );
document.write( "case 2. AE = BD = 42.  Then calculate AF and CD.\r\n" );
document.write( "\r\n" );
document.write( "AF = (3)(4) = 12\r\n" );
document.write( "CD = (6)(2) = 12       \r\n" );
document.write( "\r\n" );
document.write( "       AF = CD so there are infinitely many \r\n" );
document.write( "       solutions. \r\n" );
document.write( "\r\n" );
document.write( "---------------------------------\r\n" );
document.write( "\r\n" );
document.write( "4x + 5y = 3\r\n" );
document.write( "6x + 9y = 9\r\n" );
document.write( "\r\n" );
document.write( "3x +  7y = 2 \r\n" );
document.write( "6x + 14y = 4       \r\n" );
document.write( "\r\n" );
document.write( "A = 4, B = 5, C = 3, D = 6, E = 9, F = 9 \r\n" );
document.write( "\r\n" );
document.write( "Calculate AE and BD.  \r\n" );
document.write( "\r\n" );
document.write( "AE = (4)(9) = 36\r\n" );
document.write( "BD - (5)(6) = 30\r\n" );
document.write( "\r\n" );
document.write( "This is case 1, so there is exactly one \r\n" );
document.write( " solution.\r\n" );
document.write( "\r\n" );
document.write( "---------------------------------\r\n" );
document.write( "\r\n" );
document.write( " 6x + 11y = 12\r\n" );
document.write( "12x + 22y = 10\r\n" );
document.write( "\r\n" );
document.write( "A = 6, B = 11, C = 12, D = 12, E = 22, F = 10 \r\n" );
document.write( "\r\n" );
document.write( "Calculate AE and BD.  \r\n" );
document.write( "\r\n" );
document.write( "AE = (6)(22) = 132\r\n" );
document.write( "BD - (11)(12) = 132\r\n" );
document.write( "\r\n" );
document.write( "This is case 2:\r\n" );
document.write( "\r\n" );
document.write( "case 2. AE = BD = 132.  Then calculate AF and CD.\r\n" );
document.write( "\r\n" );
document.write( "AF = (6)(10) = 60\r\n" );
document.write( "CD = (12)(12) = 144       \r\n" );
document.write( "\r\n" );
document.write( "       AF ¹ CD so there are \r\n" );
document.write( "       no solutions. \r\n" );
document.write( "\r\n" );
document.write( "---------------------------------\r\n" );
document.write( "\r\n" );
document.write( "0.3x + 0.7y = 1.2\r\n" );
document.write( "  6x +  14y =  24\r\n" );
document.write( "       \r\n" );
document.write( "A = 0.3, B = 0.7, C = 1.2, D = 6, E = 14, F = 24 \r\n" );
document.write( "\r\n" );
document.write( "Calculate AE and BD.  \r\n" );
document.write( "\r\n" );
document.write( "AE = (0.3)(14) = 4.2\r\n" );
document.write( "BD - (0.7)(6) = 4.2\r\n" );
document.write( "\r\n" );
document.write( "This is case 2:\r\n" );
document.write( "\r\n" );
document.write( "case 2. AE = BD = 4.2.  Then calculate AF and CD.\r\n" );
document.write( "\r\n" );
document.write( "AF = (0.3)(24) = 7.2\r\n" );
document.write( "CD = (1.2)(6) = 7.2       \r\n" );
document.write( "\r\n" );
document.write( "       AF = CD so there are infinitely many \r\n" );
document.write( "       solutions.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );