document.write( "Question 1117424: x²-xy=3
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Algebra.Com's Answer #732498 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "   = 3     (1)\r\n" );
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document.write( " = 9     (2)\r\n" );
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document.write( "Right side of (2) is 9 = 3*3.  Replace one factor of 3 by the left side of (1).  You will get\r\n" );
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document.write( " = ,   or, equivalently\r\n" );
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document.write( " = 0.    (3)  \r\n" );
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document.write( "Now factor left side of (3) to get\r\n" );
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document.write( "(x-2y)*(3x+y) = 0.\r\n" );
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document.write( "Thus EITHER  x-2y = 0  OR  3x+y = 0.\r\n" );
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document.write( "Lets consider each case separately.\r\n" );
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document.write( "1)  x-2y = 0  ====>  x = 2y   ====>  substitute it into eq(1)  ====>   = 3  ====>   = 3  \r\n" );
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document.write( "              ====>   =   ====>  y = +/-  = +/- .\r\n" );
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document.write( "              If y =    <--->  x = ,    and both equations (1) and (2) are satisfied.\r\n" );
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document.write( "              If y =   <--->  x = ,   and both equations (1) and (2) are satisfied.\r\n" );
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document.write( "2)  3x+y = 0  ====>  y = -3x  ====>  substitute it into eq(1)  ====>   = 3    ====>   = 3  \r\n" );
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document.write( "              ====>   = 3/4  ====>  x = +/- .\r\n" );
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document.write( "              \r\n" );
document.write( "              If x =    <--->  y = ,    and both equations (1) and (2) are satisfied.\r\n" );
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document.write( "              If x =   <--->  y = ,     and both equations (1) and (2) are satisfied.\r\n" );
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document.write( "Answer.  The system (1), (2) has four solutions  (x,y) = (,),  (,),  (,),  (,). \r\n" );
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