It looks like you have a system of equations involving multiple variables. However, it seems like there might be some formatting issues in the way the equations are written. I will try to clarify and rewrite them in a more understandable format:

You appear to have two equations:

1. $z = f(x, y) = ax + by + c$
2. $z = a e^{-(ax + by)}$

From this, we can see that there are two expressions for $z$, one in terms of $x$ and $y$ as linear terms and one involving an exponential function. If you're looking to solve this system, we would set the right-hand sides equal to each other:

$ax + by + c = a e^{-(ax + by)}$

If you'd like to proceed with solving for specific variables or need more explanation, let me know!

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Would you like further details on:

1. Solving the system of equations?
2. Analyzing the behavior of the equation as $x$ and $y$ change?
3. Discussing methods for handling exponential and linear terms together?
4. Finding a specific solution for given values of $a$, $b$, and $c$?
5. Exploring numerical methods for this type of equation?

Tip:

When dealing with systems of equations, it's often helpful to use substitution or numerical methods, especially when one equation involves an exponential term like this one!