key term - Subtracting Equations

Definition

Subtracting equations is a method used to solve systems of linear equations by eliminating one of the variables. This technique involves adding or subtracting the equations to cancel out one of the variables, allowing the remaining variable to be solved for and the solution to the system to be found.

5 Must Know Facts For Your Next Test

1. The goal of subtracting equations is to eliminate one of the variables, allowing the remaining variable to be solved for.
2. To subtract equations, the coefficients of the variable to be eliminated must be opposite in sign and the same in absolute value.
3. Subtracting the equations results in a new equation with one variable, which can then be solved to find the value of that variable.
4. Once one variable is found, the value can be substituted back into one of the original equations to solve for the remaining variable.
5. Subtracting equations is a powerful technique for solving systems of linear equations, especially when the coefficients of the variables are different in the original equations.

Review Questions

• Explain the purpose of subtracting equations in the context of solving systems of linear equations.
  • The purpose of subtracting equations in the context of solving systems of linear equations is to eliminate one of the variables. By adding or subtracting the equations, the coefficients of one of the variables can be made to cancel out, leaving a new equation with only one variable. This allows the remaining variable to be solved for, and then the solution can be substituted back into one of the original equations to find the value of the other variable. Subtracting equations is a key technique in the elimination method for solving systems of linear equations.
• Describe the necessary conditions for successfully subtracting equations to eliminate a variable.
  • To successfully subtract equations to eliminate a variable, the coefficients of the variable to be eliminated must be opposite in sign and the same in absolute value. For example, if one equation has the variable $x$ with a coefficient of 2, and the other equation has the variable $x$ with a coefficient of -2, then subtracting the equations will result in the $x$ terms canceling out. This allows the remaining variable to be solved for, and then the solution can be used to find the value of the eliminated variable.
• Analyze the steps involved in using the subtracting equations method to solve a system of linear equations.
  • The steps involved in using the subtracting equations method to solve a system of linear equations are: 1) Identify the variable to be eliminated, and ensure that the coefficients of that variable in the two equations have opposite signs and the same absolute value. 2) Subtract the equations to eliminate the selected variable, resulting in a new equation with only one remaining variable. 3) Solve the new equation to find the value of the remaining variable. 4) Substitute the found value back into one of the original equations to solve for the eliminated variable. 5) Verify that the solution satisfies both original equations in the system.

Related terms

Elimination Method:

A technique for solving systems of linear equations by adding or subtracting the equations to eliminate one of the variables.

Linear Equations:

An equation in which the variables are raised to the first power and the equation forms a straight line when graphed.

System of Equations:

A set of two or more linear equations that share the same variables and must be solved simultaneously.