We replace x by (x+h) and y by (y+k)
There is no need to multiply everything out yet, so we just list
the first degree terms:
Group the x terms and the y-terms and factor out x and y:
The first degree terms will vanish (become 0) if the coefficients of x and y
are both 0. So we set them equal 0:
We solve that system by elimination or substitution
and get h=2, k=4
That simplifies to
So we shift the graph 2 units left and 4 units down and that
will eliminate the first degree terms, leaving only terms of
degrees 0 and 2.
Edwin