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Chapter 7: Problem 97

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

Short Answer

Expert verified
The addition method is generally easier to use when one variable's coefficients in both equations are the same or can be easily made to be the same, provided it does not result in complex fractions.

Step by step solution

01

Understanding the Addition (Elimination) Method

The addition (or elimination) method to solve a system of equations involves adjusting the equations (if necessary) so that one of the variables has the same coefficient in both equations, and then either adding or subtracting the equations to eliminate that variable. This is usually more straightforward when the coefficients of one variable in both equations are the same or if they can be made the same by easily multiplying one or both equations by a suitable number.
02

Understanding the Substitution Method

The substitution method involves rearranging one equation to express one variable in terms of the other, and then substituting this expression in the other equation. This method can be more intuitive if one equation can be easily rearranged to express one variable as a simple function of the other. However, if such rearrangement is complex or leads to fractions, the substitution method can be cumbersome.
03

Identifying When to Use the Addition Method

The addition method is generally easier to use when the coefficients of one variable are the same in both equations or can be made the same easily without resulting in complex fractions. For example: For a system of equations like 3x + 2y = 5 and 6x + 4y = 10, it would be easier to use the addition method because you could simply subtract the second equation from the first to eliminate the 'x' variable.

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