Find the Domain 3x+1/3y=21

Problem

3*x+1/(3*y)=21

Solution

1. Identify the variables in the equation. The equation involves two variables, x and y In the context of a function or relation, the domain typically refers to the set of all possible values for the independent variable x

2. Analyze the expression for restrictions. The term 1/(3*y) contains a variable in the denominator. A fraction is undefined when its denominator is equal to zero.

3. Set the denominator equal to zero to find the excluded value for y

3*y=0

y=0

4. Solve the original equation for y to see if any restrictions on x arise.

1/(3*y)=21−3*x

3*y=1/(21−3*x)

y=1/(3*(21−3*x))

5. Determine the restriction for x by setting the new denominator to zero.

3*(21−3*x)=0

21−3*x=0

3*x=21

x=7

6. Conclude that x can be any real number except for 7 as x=7 would result in a division by zero in the expression for y

Final Answer

Domain:{[x∈ℝ,x≠7]}

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