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Algebra is a branch of mathematics that uses symbols instead of numbers to express mathematical relationships. These symbols, often letters, are known as variables because they stand for numbers that can change.
The core idea behind algebra is to find unknown values by connecting them with known ones using mathematical operations. In this context, equations like the given one, \(2x + 3y = 4\), serve as relationships between the variables \(x\) and \(y\).
Solving algebraic equations often involves rearranging the terms to find the value of one variable in relation to others. This provides a way to express complex relationships in a simplified, general form. It is crucial to practice these sorts of transformations to become comfortable with algebraic manipulation.

Variable isolation is the process of rearranging an equation to get one variable alone on one side of the equation. This method simplifies an equation by making it easier to work with one variable at a time.

• To isolate a variable, you usually perform inverse operations, such as addition or subtraction, and multiplication or division.
• For the equation \(2x + 3y = 4\), the goal was to isolate \(y\).

We subtracted \(2x\) from both sides to get \(3y = 4 - 2x\).
Next, we divided the whole equation by 3 to solve for \(y\), giving us \(y = \frac{4 - 2x}{3}\).
Performing these steps allows us to express \(y\) independently and view how it changes concerning \(x\). This step-by-step process is key to solving many algebraic problems.

In mathematics, an implicit function is defined through an equation not explicitly solved for one variable in terms of another.
The original exercise, \(2x + 3y = 4\), is an example of an implicit equation involving two variables, \(x\) and \(y\).

When solving for \(y\) in terms of \(x\), we are converting this implicit form to an explicit one.

This change makes it clearer how one variable is directly determined by another.

In this case, \(y = \frac{4 - 2x}{3}\) tells us exactly how \(y\) depends on \(x\). Converting implicit equations into explicit functions is an essential aspect of algebra and is particularly useful for graphing and analyzing the behavior of functions.