Find the Domain 45x+55y=6900

Problem

45*x+55*y=6900

Solution

1. Identify the type of equation. The equation 45*x+55*y=6900 is a linear equation in two variables.

2. Determine the context of the variables. In a general mathematical context, a linear function y=ƒ(x) is defined for all real numbers unless specified otherwise by a real-world constraint (such as x representing a quantity that cannot be negative).

3. Solve for y to express the equation as a function of x

55*y=6900−45*x

4. Divide by 55 to isolate y

y=(6900−45*x)/55

5. Analyze the resulting expression. Since the expression is a polynomial (specifically a linear function), there are no values of x that would result in division by zero or the square root of a negative number.

6. Conclude that the domain is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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