CramX Logo

Q
QuestionMathematics

Determine whether the following equation represents a linear or non-linear function. Provide steps if possible. 2x+ 3y= 9xy
12 months agoReport content

Answer

Full Solution Locked

Sign in to view the complete step-by-step solution and unlock all study resources.

Step 1:
: Identify the given equation.

The given equation is $2x + 3y = 9xy$.

Step 2:
: Understand the difference between linear and non-linear functions.

A linear function has a degree of 1, meaning the highest power of the variable(s) in the function is 1. A non-linear function has a degree greater than 1, meaning the highest power of the variable(s) in the function is greater than 1.

Step 3:
: Examine the given equation for the degree.

This indicates that the equation does not represent a simple sum of terms with only $x$ and $y$ but also their product $xy$.
Consequently, the degree of the equation cannot be 1, and the equation does not represent a linear function.

Step 4:
: Confirm the non-linearity of the function.

However, we have already determined that the equation does not represent a linear function due to the presence of the $xy$ term.
Since this equation does not fit the standard form of a second-degree polynomial, it is not a quadratic function either. Therefore, we can conclude that the given equation represents a non-linear function.

Final Answer

The given equation $2x + 3y = 9xy$ represents a non-linear function.