document.write( "Question 1175906: Please help me solve 3x + y=3
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Algebra.Com's Answer #801700 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " The setup in the post by @josgarithmetic is INCORRECT, so ignore his post.\r
\n" ); document.write( "\n" ); document.write( " I came to bring a correct solution.\r
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document.write( "    3x + y = 3     (1)\r\n" );
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document.write( "    xy = -6        (2)\r\n" );
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document.write( "From equation (1), express y = 3 - 3x = 3*(1-x)  and substitute it into equation (2). You will get\r\n" );
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document.write( "    3x*(1-x) = -6.\r\n" );
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document.write( "Simplify it step by step, making equivalent transformations\r\n" );
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document.write( "    x*(1-x) = -2\r\n" );
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document.write( "    x*(x-1) = 2\r\n" );
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document.write( "    x^2 - x - 2 = 0\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (x-2)*(x+1) = 0   \r\n" );
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document.write( "The roots are  x= 2  and  x= -1.\r\n" );
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document.write( "To get y, consider these two cases separately.\r\n" );
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document.write( "    a)  If x = 2,  then  y = 3*(1-x) = 3*(1-2) = 3*(-1) = -3.\r\n" );
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document.write( "    b)  If x= -1,  then  y = 3*(1-x) = 3*(1-(-1)) = 3*2 = 6.\r\n" );
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document.write( "ANSWER.  There are two solutions:  a) x=2,  y= -3   and   b) x= -1, y= 6.\r\n" );
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