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In this section, we'll look at the technique known as 'isolation of variable'. This is one of the most important steps in solving linear equations.

The goal is to rearrange the equation to get one variable by itself on one side of the equation. For instance, in the exercise provided, the goal is to isolate the variable y.

We start with the equation:
\[ 2y - 3x = 6 \]
To isolate 'y', we need to move the term involving 'x' to the other side.

We do this by adding 3x to both sides:\[ 2y - 3x + 3x = 6 + 3x \]
That simplifies to:\[ 2y = 3x + 6 \]
Now, 'y' is isolated on one side of the equation.

This process is crucial because it helps to simplify the equation and set the stage for solving for the variable.

Next, let's talk about 'simplifying expressions'. This step is all about making the equation easier to work with by combining like terms and reducing fractions.

After isolating the variable, the equation was:\[ 2y = 3x + 6 \]
To solve for 'y', we need to perform one more step. We divide both sides by 2 to solve for 'y':\[ y = \frac{3x + 6}{2} \]
While this is correct, it can be simplified further. In the numerator, we can split the fraction:\[ y = \frac{3x}{2} + \frac{6}{2} \]
This simplifies to:\[ y = \frac{3}{2}x + 3 \]
Now, the expression is simplified and easier to interpret.

It is always important to simplify the expression to its simplest form to facilitate understanding and confirm the accuracy of the result.

Lastly, let's understand what 'linear equations' are. A linear equation is an algebraic equation in which each term is a constant or the product of a constant and a single variable. In simpler terms, it forms a straight line when graphed.

An example of a linear equation from our exercise is:
\[ 2y - 3x = 6 \]
Linear equations often involve operations of addition, subtraction, multiplication, and division applied to variables and constants. They do not involve exponents, radicals, or variables multiplied by each other.

The solution of a linear equation in two variables (like this one) is represented as a line in a two-dimensional space, where each pair (x,y) that satisfies the equation lies on this line.

Understanding linear equations helps in solving more complex algebraic equations and provides a foundation for other mathematical concepts. This basic knowledge ensures you can tackle more advanced topics with confidence.