Elimination

Definition

Elimination is a method for solving systems of equations where one variable is removed by adding or subtracting the equations. This process simplifies the system to a single-variable equation, which can then be solved.

5 Must Know Facts For Your Next Test

1. Elimination involves aligning terms with the same variables and coefficients to facilitate cancellation.
2. Multiplying one or both equations by constants may be necessary to align coefficients for elimination.
3. The elimination method can be used for both linear and nonlinear systems of equations.
4. After eliminating one variable, substitution may still be needed to find the value of the remaining variables.
5. Elimination is particularly useful when dealing with systems that are easily manipulated into equivalent forms.

Review Questions

• What initial steps must you take to align coefficients before using elimination?
• How do you decide whether to add or subtract equations in the elimination method?
• Can elimination be used on nonlinear systems of equations? Provide an example.

Related terms

Substitution: A method for solving systems of equations where one equation is solved for one variable in terms of another and then substituted into the other equation.

System of Equations: A set of two or more equations with the same variables that are considered simultaneously.

Nonlinear System: A system of equations in which at least one equation is not linear, involving variables raised to powers other than one or products of variables.