Question 1180470
 One solution to the system of equations : 

{{{y= mx^2 +nx +n }}}
{{{y= nx^2 -mx +n }}}

({{{-2}}},{{{11}}}) 

{{{11= m(-2)^2 +(-2)_n +n }}}
{{{11= n(-2)^2 -(-2)m +n }}}
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{{{11= 4m -2n +n }}}
{{{11= 4n +2m +n }}}

=>{{{ 4m-2n +n=  4n +2m +n }}}
{{{ 4m-2n =  4n +2m  }}}
{{{ 2m-n =  2n +m  }}}
{{{ 2m-n -2n -m=0  }}}
{{{ m -3n =0  }}}
{{{ m =3n   }}}

go to

{{{11= 4m -2n +n }}}, substitute {{{m}}}

{{{11= 4*3n -2n +n }}}
{{{11= 12n -2n +n }}}
{{{11= 11n }}}
{{{n=1}}}

=>{{{ m =3*1   }}}=>{{{ m =3   }}}

check:

{{{y= 3x^2 +x +1 }}}
{{{y= x^2 -3x +1 }}}

{{{ drawing( 600, 600, -10, 10, -10, 15,
circle(-2,11,.12), locate(-2,11,p(-2,11)),
graph( 600, 600, -10, 10, -10, 15,3x^2 +x +1, x^2 -3x +1)) }}}