document.write( "Question 1106909: determine whether each system of linear equations has a) one and only one solution b) infinitely solutions c) no solution
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Algebra.Com's Answer #721907 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "determine whether each system of linear equations has a) one and only one solution b) infinitely solutions c) no solution
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document.write( "-10x + 15y = -3     (1)\r\n" );
document.write( "  4x -  6y = -3     (2)\r\n" );
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document.write( "Divide the equation (1) by (-5)  (both sides).\r\n" );
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document.write( "Divide the equation (2) by 2  (both sides).  You will get and equivalent system\r\n" );
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document.write( "  2x  - 3y =    (1')\r\n" );
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document.write( "  2x - 3y =     (2')\r\n" );
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document.write( "Left sides of equations (1') and (2') are IDENTICAL, which means that left sides are equal at each values of x and y.\r\n" );
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document.write( "But right sides ARE NOT EQUAL.\r\n" );
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document.write( "It means that the system (1'),(2')  HAS NO SOLUTIONS.\r\n" );
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document.write( "Then the equivalent system (1),(2)  HAS NO SOLUTIONS, too.\r\n" );
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