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The pair of equation I need to solve is

  1. $x^2+12x+y^2-4y=24$
  2. $x^2-6x+y^2+8y=25$

I have no idea on how to do these kinds of problems (may be by elimination?)

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up vote 5 down vote accepted

Subtract the second equation from the first (collect like terms), get a linear equation, solve for $y,$ substitute back, solve the quadratic for $x,$ substitute back for $y.$

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HINT : Notice that the two equations have the same form as $$1\cdot x^2+ax+1\cdot y^2+by=c.$$ So, if you subtract one from the other, then you'll get a form $y=dx+e.$

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