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Understanding algebraic expressions is fundamental in solving linear equations. An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like the letter 'y' in our exercise), and operators (such as addition and subtraction). In the given problem, \(55 - 5y = 9y + 27\), we have a typical algebraic expression where numbers and variables are combined.
For successfully tackling these expressions, it’s critical to recognize the parts that can be manipulated to solve for a variable. In our exercise, you see numbers and multiple instances of the variable 'y'; this represents a common scenario you'll encounter in algebra. Always remember, the goal is to manipulate the expression in a way that the variable you’re solving for is isolated on one side of the equation.

Combining like terms is one of the essential strategies for simplifying algebraic expressions. Like terms are terms that have the same variable raised to the same power, even if they have different coefficients. For instance, \(5y\) and \(-9y\) are like terms.
In our exercise, 'like terms' across both sides of the equation were identified and combined to simplify the equation further. Specifically, the \(5y\) on the left side and the \(9y\) on the right side of the equation were combined in the process to bring all variable terms to one side, making it easier to isolate the variable. This is a crucial step, as it reduces the equation down to its simplest form, allowing for easier manipulation in the subsequent steps.

Isolation of variables plays a pivotal role in solving linear equations. It involves rearranging the equation so that the desired variable stands on its own on one side of the equality sign.
In practice, you'll aim to move all terms containing the variable to one side and all the constant terms to the other. This was visible in the exercise when the constant '27' was moved to the other side of the equation, leaving 'y' terms on the right side. Then, by dividing both sides of the equation by the coefficient of 'y', which in this case was '14', we arrive at the value of the isolated variable. This process of simplification and manipulation reveals the value of 'y' with a straightforward, unambiguous numerical result.