Final answer:
Fill in the blanks with 'opposite' for subtraction and 'identical' for addition to eliminate algebraic terms with coefficients that allow for simplification.
Step-by-step explanation:
If the variables have opposite coefficients, use subtraction to eliminate the terms. If the variables have identical coefficients, use addition to eliminate the terms.
In algebra, simplifying equations often involves combining like terms and eliminating variables to solve for a specific unknown. When two algebraic expressions are set equal to each other, manipulating the equation by either addition or subtraction can help isolate the variable.
For instance, if you have an equation where the variable terms have opposite coefficients, like 3x and -3x, subtracting one from the other will eliminate the x term completely. On the other hand, if the variable terms have identical coefficients, such as 4y and 4y, adding them together will eliminate the y term, as they will either add up to double the coefficient or cancel each other out if one is negative.
Once the elimination is done, you must always check your answer to ensure that it is reasonable within the context of the original equation or problem.