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Given the equations $F(x,y,z,w)=0$ and $G(x,y,z,w)=0$ . Where $F$ and $G$ have continuous first partial derivatives, $(\frac{\partial x}{\partial z})_w$= ?

I think this question was asked earlier.But I do not understand anything from the answers.I tried to solve.I obtained this part.I think $x$ and $y$ are depend and $z$,$w$ are independent by theorem then

$F_1 (\frac{\partial x}{\partial z})$$+$$F_2 (\frac{\partial y}{\partial z})$$+$$F_3$=$0$

$G_1 (\frac{\partial x}{\partial z})$$+$$G_2 (\frac{\partial y}{\partial z})$$+$$G_3$=$0$

$F_4 (\frac{\partial w}{\partial z})$ and $G_4 (\frac{\partial w}{\partial z})$$ not important because w is independent.

How can I continue ?

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    What do you mean by the notation $\left(\dfrac{\partial x}{\partial z}\right)_w$? Is it $\dfrac{d^2x}{dwdz}$ ? – 2017-01-10
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    no. it is systems of equations by implicit functions – 2017-01-10
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    So what is $\left(\dfrac{\partial x}{\partial z}\right)_w$? – 2017-01-10
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    Its the derivative of x with respect to z keeping w constant I think, I feel its more common in physics (like in thermodynamics) to explicitly mention the variable being kept constant. From what I gather x doesn't depend on y? – 2017-01-10
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    not physics of course the physics depend on calculus but it is question of calculus.actually i can use cramer rule but i don't do it .it is complicated – 2017-01-10

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