document.write( "Question 1180470: One solution to the system of equations : y= mx^2 +nx +n and y= nx^2 -mx +n is (-2,11) . Algebraically determine the values of m and n.
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Algebra.Com's Answer #810138 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "One solution to the system of equations : y= mx^2 +nx +n and y= nx^2 -mx +n is (-2,11) . Algebraically determine the values of m and n.
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document.write( "First, substitute the solution x= -2, y= 11 into the first equation.  You will get then\r\n" );
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document.write( "    11 = m*(-2)^2 + n*(-2) + n,\r\n" );
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document.write( "or, equivalently,\r\n" );
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document.write( "    11 = 4m - n.    (1)\r\n" );
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document.write( "Next, substitute the solution x= -2, y= 11 into the second equation.  You will get then\r\n" );
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document.write( "    11 = n*(-2)^2 - m*(-2) + n,\r\n" );
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document.write( "or, equivalently,\r\n" );
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document.write( "    11 = 5n + 2m.    (2)\r\n" );
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document.write( "Equations (1) and (2) form the system of 2 equations in 2 unknowns m and n to solve. \r\n" );
document.write( "I will re-write the system in the standard form\r\n" );
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document.write( "    4m -  n = 11      (1')\r\n" );
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document.write( "    2m + 5n = 11      (2')\r\n" );
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document.write( "To solve the system, from equation (1') express  n = 4m-11  and substitute it into (2').  You will get\r\n" );
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document.write( "    2m + 5*(4m-11) = 11\r\n" );
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document.write( "Simplify and solve\r\n" );
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document.write( "    2m + 20m - 55 = 11\r\n" );
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document.write( "    22m            = 11 + 55 = 66\r\n" );
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document.write( "      m                      = 66/22 = 3.\r\n" );
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document.write( "Finally, from n = 4m-11 you find  n = 4*3-11 = 12-11 = 1.\r\n" );
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document.write( "ANSWER.  n = 1;  m = 3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "You may CHECK it on your own, that my solution is correct, by substituting the found values
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