How to solve the following pair of equation.

Question

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?)

Answer 1

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 $y.$

Answer 2

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 $y=dx+e.$