Substitution method

Definition

The substitution method is a technique for solving systems of equations by substituting one equation into another. This transforms the system into a single-variable equation that can be solved more easily.

5 Must Know Facts For Your Next Test

1. It is often used when one of the equations in the system is already solved for one variable.
2. The method involves replacing one variable with an equivalent expression from another equation.
3. After substitution, you solve for the remaining variable and then back-substitute to find the other variable.
4. Substitution can simplify solving systems where equations are linear and involve two variables.
5. It is especially useful for solving word problems where relationships between quantities can be expressed as linear equations.

Review Questions

• What are the steps involved in using the substitution method to solve a system of linear equations?
• How do you decide which equation to use for substitution in a given system?
• Can the substitution method be used if both equations are not initially solved for one variable? If so, how?

Related terms

System of Linear Equations:

A set of two or more linear equations involving the same set of variables.

Elimination Method:

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

Consistent System:

A system of equations that has at least one solution.