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Chapter 7: Problem 71

When is it easier to use the addition method rather than the substitution method to solve a system of equations?

Short Answer

Expert verified
It is easier to use the addition method when the coefficients of one of the variables in both equations are identical or additive inverses, allowing immediate cancellation of that variable upon addition or subtraction. If the system of equations is such that it can be easily manipulated for addition or subtraction to eliminate a variable, the addition method proves to be easier than the substitution method.

Step by step solution

01

Understanding the Addition Method

Addition method, also known as the elimination method, involves adding or subtracting the equations in order to eliminate one of the variables. This method is especially useful when the coefficients of one of the variables in both equations are the same or additive inverses, allowing easy cancellation of that variable.
02

Understanding the Substitution Method

The substitution method involves solving one of the equations for one variable in terms of the other variable, and then substituting this expression into the other equation. This method can be efficient when one equation is already solved for one of the variables or can be easily manipulated to solve for one variable. It is also useful when the equations can't be readily added or subtracted to eliminate a variable.
03

Determining When to Use the Addition Method

The addition method becomes easier to use over the substitution method in scenarios where the coefficients of one of the variables in both equations are either identical or additive inverses (for example, one is positive and the other is negative but they have the same absolute value). This allows for immediate cancellation of that variable upon addition or subtraction. Therefore, if the system of equations is such that it can be manipulated easily for addition or subtraction to eliminate a variable, the addition method proves to be easier than the substitution method.

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