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In algebra, combining like terms is a fundamental concept that simplifies expressions. It involves adding or subtracting terms with the same variable. For example, in the expression \(-9y + 5y - 7y\), all terms include the variable 'y'.
This means they are like terms and can be combined. To do this, focus on the numerical part of each term, which are the coefficients. Combine these coefficients to simplify the expression.
Always remember, only terms with identical variables and exponents can be combined. Terms without variables, known as constant terms, can be combined with other constants.
Identifying and combining like terms simplifies algebraic expressions, making them easier to understand and solve.

Coefficients are the numbers placed in front of variables in algebraic expressions. They tell us how many units of each variable we have. In the expression \(-9y + 5y - 7y\), the coefficients are -9, 5, and -7, respectively.
When combining like terms, pay attention to these coefficients. They indicate how much of each variable is present. Adding or subtracting these coefficients helps simplify expressions. For example, combining the coefficients in \(-9y + 5y - 7y\) gives \(-11y\).
The coefficient -11 shows that there are 11 negative 'y' units in this simplified form.
Understanding coefficients is key for simplifying expressions and solving equations effectively.

Variables are symbols, usually letters, that represent unknown values in algebraic expressions. They allow expressions and equations to generalize mathematical statements for different possible values.
In the exercise example, the variable is 'y', appearing in all terms as \(-9y\), 5y, and \(-7y\). These 'y' elements are placeholders for numbers that we don't yet know.
The beauty of variables is that they can take on different values, making algebra a powerful tool for representing real-world situations mathematically.
When simplifying expressions like \(-9y + 5y - 7y\), we focus on combining coefficients first.
However, it's the variables that let us know which terms can be combined together, underlining their importance in algebra.