Addition method

Definition

The addition method, also known as the elimination method, is a technique used to solve systems of linear equations. It involves adding or subtracting the equations to eliminate one variable, simplifying the system to a single equation with one variable.

5 Must Know Facts For Your Next Test

1. The goal of the addition method is to eliminate one variable by combining the equations.
2. Equations may need to be multiplied by constants to align coefficients before adding or subtracting.
3. After eliminating a variable using addition or subtraction, solve for the remaining variable.
4. The solution obtained from solving for one variable should be substituted back into one of the original equations to find the other variable.
5. The resulting pair $(x, y)$ represents the point of intersection of the two lines represented by the original equations.

Review Questions

• What is the primary objective when using the addition method?
• When might you need to multiply an equation by a constant during this process?
• How do you find the second variable after eliminating one using addition?

Related terms

Substitution Method: A technique for solving systems of equations where one equation is solved for one variable and then substituted into another equation.

System of Linear Equations: A set of two or more linear equations with multiple variables that are considered simultaneously.

Consistent System: A system of equations that has at least one solution.