Problem 89 - College Algebra

Question

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

Step-by-Step Solution

Answer

The addition method is easier to use than the substitution method when the coefficients of one of the variables are the same or opposites in the system of equations.

Step 1: Understanding Addition Method

The addition method, also known as the elimination method, works best when you want to eliminate one of the variables by adding or subtracting the two equations. This is easier to do when the coefficients of one of the variables are the same or opposites in the two equations, such as \(2x + 3y = 7\) and \(-2x - y = 3\).

Step 2: Understanding Substitution Method

The substitution method works best when you easily solve one of the equations for one variable in terms of the other. This is easier when one of the variables has a coefficient of 1 or -1, such as \(x + 3y = 7\) and \(2x - y = 3\).

Step 3: Comparing Addition and Substitution Method

The addition method might be easier to use than the substitution method when the given system of equations has terms that match each other or are opposites. In these cases, adding or subtracting the equations immediately eliminates one variable, making it straightforward to find the unknowns.