Solving for $dx/dt$

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"Suppose that $x=x(t)$ and $y=y(t)$ are both functions of $t$. If $y^2+xy−3x=−5$, and $dy/dt=−3$ when $x=3$ and $y=1$, what is $dx/dt$?"

So I differentiated it and got $2y(dy/dt) + x(dy/dt) + y(dx/dt) -3(dx/dt) = 0$.

I then plugged in all the values and got:

$2(1)(-3) + (3)(-3) + (1)(dx/dt) -3(dx/dt) = 0$

$-4(dx/dt) = 15$ and therefore $dx/dt = -15/4$, but this was not the correct answer..

Does anyone know where I went wrong? I'm thinking it was in the intial differentiation but I'm struggling to figure out which part.

Any help?