Identifying Linear Equations in Two Variables

Q1. Determine if the given equation is a linear equation in two variables.

Given equation: $8x^2 - 6y = 9$

Background

Topic: Linear Equations in Two Variables

This question tests your understanding of what makes an equation linear and how to identify whether an equation with two variables fits the definition of a linear equation.

Key Terms and Concepts:

• Linear Equation in Two Variables: An equation of the form $Ax + By = C$, where $A$, $B$, and $C$ are constants, and both $x$ and $y$ have exponents of 1 (no higher powers or products of variables).

• Nonlinear Equation: An equation where at least one variable is raised to a power other than 1, or variables are multiplied together.

Step-by-Step Guidance

1. Examine the given equation: $8x^2 - 6y = 9$.

2. Identify the exponents of each variable. In a linear equation, both $x$ and $y$ should have an exponent of 1.

3. Check if there are any terms where a variable is raised to a power other than 1, or if variables are multiplied together.

4. Compare the structure of the given equation to the standard form of a linear equation: $Ax + By = C$.

Try solving on your own before revealing the answer!