Implicit differentiation question

Question

If 2x^2+5x+xy =1 and y(1)= -6

find y'(1)=?

Answer 1

So considering that (1, -6) is a point on the curve and we are asking for the slope at x = 1 as well, then

y'(1) = [-4(1) - 5 - (-6)]/1 = -4 - 5 + 6 = -3

Answer 2

2x²+5x+xy=1

Take the derivative of both sides

4x+5+xdy/dx+y=0

xdy/dx = -4x-5-y

dy/dx =-(4x+5+y)/x

y'(1)=-(4(1)+5+(-6))/1 = -3