Solution set

Definition

A solution set is the set of all possible values that satisfy a given equation or system of equations. It represents all the solutions that make the equation(s) true.

5 Must Know Facts For Your Next Test

1. For a linear equation in one variable, the solution set typically contains one value unless the equation has no solution or infinitely many solutions.
2. In a system of linear equations with three variables, the solution set can be a single point, a line, a plane, or empty.
3. To find the solution set of a system of equations, methods such as substitution, elimination, and matrix operations can be used.
4. The consistency and dependency of a system determine whether its solution set is unique, infinite, or nonexistent.
5. Graphical representation can help visualize the solution set for systems of equations.

Review Questions

• What does it mean if an equation's solution set is empty?
• How do you determine the solution set for a linear equation in one variable?
• What are some methods to find the solution set for a system of three linear equations?

Related terms

Linear Equation: An algebraic equation in which each term is either a constant or the product of a constant and a single variable.

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

Matrix Operations: \text{Operations such as addition, subtraction, multiplication, and inversion applied to matrices to solve systems of equations.}