Find the Domain 4x-3y+z=18

Problem

4*x−3*y+z=18

Solution

1. Identify the type of equation provided. The equation 4*x−3*y+z=18 represents a linear equation in three variables, which defines a plane in three-dimensional space ℝ3

2. Analyze the constraints on the variables. In a linear polynomial equation, there are no square roots of negative numbers, no denominators that could be zero, and no logarithms of non-positive numbers.

3. Determine the possible values for the independent variables. Since there are no restrictions, the variables x and y (treating z as a function of x and y can take any real number value.

4. State the domain in set-builder or interval notation. The domain is the set of all ordered pairs (x,y) such that x and y are real numbers.

Final Answer

Domain={(x,y)|x∈ℝ,y∈ℝ}

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