- #1

- 798

- 1

## Homework Statement

Consider the system of equations

[tex]x^2y+za+b^2=1[/tex]

[tex]y^3z+x-ab=0[/tex]

[tex]xb+ya+xyz=-1[/tex]

1. Can the system be solved for [tex]x, y, z[/tex] as functions of [tex]a[/tex] and [tex]b[/tex] near the point [tex](x, y, z, a, b)=(-1, 1, 1, 0, 0)[/tex]?

2. Find [tex]\frac{\partial x}{\partial a}[/tex] where [tex]x=x(a, b)[/tex]

## The Attempt at a Solution

For part 1, do I merely plug in [tex](x, y, z)=(-1, 1, 1)[/tex] and then solve the system of linear equations with the variables a and be remaining in the function?

Part 2 really confuses me. My textbook has taught us one notation, and then it states a question in this format. For example, often it will say something such as [tex](\frac{\partial z}{\partial x})_w[/tex] to notify when something is independent or dependent. Can someone clarify what the question is stating?