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When solving linear equations, the first step often involves combining like terms. Like terms are terms that have the same variables raised to the same power. In this case, both \(-6y\) and \(-3y\) are like terms because they have the variable \(y\) raised to the first power.
Combining like terms helps simplify the equation and makes it easier to solve.
For \(-6y - 3y = 27\), you combine the like terms \(-6y\) and \(-3y\) by adding them together:
\(-6y - 3y = -9y\).
This reduces the equation to:
\(-9y = 27\).
Combining like terms is a critical skill in algebra as it simplifies the problem, making it less complex and easier to solve in the subsequent steps.

After combining like terms, the next step is to isolate the variable. Isolating the variable means getting the variable by itself on one side of the equation.
This makes it easier to see what value the variable equals.
From the equation \(-9y = 27\), we can isolate \(y\) by dividing both sides of the equation by \(-9\).
This division step is crucial for balancing the equation and maintaining equality.
Doing the division: \[ y = \frac{27}{-9} \].
By isolating \(y\), we simplify the equation to a form where we can easily see that \(y\) is being multiplied by \(-9\) and the solution is a simple division operation.

The final step in solving our equation involves simplifying fractions. Simplifying fractions means reducing them to their simplest form.
This makes the result easier to understand and often more meaningful in practical terms.
In our equation, we end up with the fraction \[ y = \frac{27}{-9} \].
To simplify this, you divide the numerator (27) by the denominator (-9):
\[ \frac{27}{-9} = -3 \].
Hence, the simplified solution for \(y\) is \(-3\).
Simplifying fractions is crucial in mathematics, especially in algebra, to ensure that the solutions are as straightforward and understandable as possible.
It involves basic division and is a foundational skill that helps in solving and interpreting mathematical problems correctly.