Find the Domain 2x+3y=7

Problem

2*x+3*y=7

Solution

1. Identify the type of equation. The equation 2*x+3*y=7 is a linear equation in two variables, which represents a straight line in the Cartesian plane.

2. Solve for y to express the equation as a function of x Subtract 2*x from both sides and divide by 3

3*y=−2*x+7

y=−2/3*x+7/3

3. Analyze the resulting function for restrictions. The expression −2/3*x+7/3 is a polynomial of degree 1.

4. Determine if there are any values of x that would cause division by zero or result in an undefined value. Since there are no variables in denominators and no square roots of negative numbers, the function is defined for all real numbers.

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

Final Answer

Domain: *(−∞,∞)

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