Subtraction Method

Definition

The subtraction method is a technique used to solve systems of linear equations by eliminating one of the variables through subtraction. This approach allows for the determination of the values of the variables that satisfy the given system of equations.

5 Must Know Facts For Your Next Test

1. The subtraction method is particularly useful when the coefficients of one variable in the system of equations have opposite signs.
2. To apply the subtraction method, the user must first identify the variable to be eliminated and then multiply one or both equations by a constant to make the coefficients of that variable have opposite signs.
3. After the equations are manipulated, the user can subtract the equations to eliminate the target variable and solve for the remaining variable.
4. The subtraction method can be used to solve systems of equations with two or more variables, provided that the number of equations is equal to the number of variables.
5. The subtraction method is often considered more efficient than the substitution method when dealing with systems of equations with more than two variables.

Review Questions

• Explain the basic steps involved in using the subtraction method to solve a system of linear equations.
  • To use the subtraction method to solve a system of linear equations, the first step is to identify the variable that will be eliminated. Then, the user must multiply one or both equations by a constant to make the coefficients of the target variable have opposite signs. Next, the equations are subtracted to eliminate the variable, leaving an equation with a single variable that can be solved. Finally, the value of the remaining variable is substituted back into one of the original equations to find the value of the eliminated variable.
• Describe the advantages of the subtraction method compared to the substitution method for solving systems of linear equations.
  • The subtraction method is often considered more efficient than the substitution method when dealing with systems of equations with more than two variables. This is because the subtraction method allows for the elimination of a variable without the need to isolate it, as is required in the substitution method. Additionally, the subtraction method can be applied more easily when the coefficients of the variables have opposite signs, which is a common scenario in systems of linear equations.
• Analyze the role of the augmented matrix in the subtraction method for solving systems of linear equations.
  • The augmented matrix plays a crucial role in the subtraction method for solving systems of linear equations. The augmented matrix combines the coefficients of the variables and the constants from the system of equations into a single matrix. This matrix representation allows for the efficient manipulation of the equations, such as multiplying rows by constants and subtracting rows, to eliminate variables and solve the system. The use of the augmented matrix simplifies the process of applying the subtraction method and helps to ensure that the steps are carried out accurately.

Related terms

Elimination Method:

A method for solving systems of linear equations by using addition or subtraction to eliminate one of the variables, allowing for the determination of the values of the remaining variables.

Augmented Matrix: A matrix formed by combining the coefficients of the variables and the constants from a system of linear equations, used in various methods of solving the system.

Substitution Method:

A method for solving systems of linear equations by expressing one variable in terms of the other and then substituting the expression into the other equation to solve for the remaining variable.