Find the Domain z=5x+3y

Problem

z=5*x+3*y

Solution

1. Identify the type of function provided. The expression z=5*x+3*y is a linear function of two variables, x and y

2. Check for restrictions such as denominators that could be zero, square roots of negative numbers, or logarithms of non-positive numbers.

3. Determine that there are no such restrictions in this polynomial expression, meaning x and y can be any real numbers.

4. State the domain as the set of all ordered pairs (x,y) in the two-dimensional real plane.

Final Answer

Domain={(x,y)|x∈ℝ,y∈ℝ}

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