Solution set

Definition

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

5 Must Know Facts For Your Next Test

1. In a linear equation in one variable, the solution set typically contains a single value.
2. For systems of linear equations, the solution set can be a single point, infinitely many points (a line or plane), or empty.
3. The solution set for an inequality includes all values that satisfy the inequality and is often represented on a number line or coordinate plane.
4. To find the solution set for systems of equations with three variables, methods such as substitution, elimination, or matrix operations are used.
5. A consistent system has at least one solution in its solution set; an inconsistent system has no solutions.

Review Questions

• What does the term 'solution set' mean in relation to a given equation?
• How would you describe the solution set for a system of linear equations with three variables?
• What methods can be used to determine the solution set of systems with multiple variables?

Related terms

Linear Equation: An equation that makes a straight line when it is graphed. Typically in the form $ax + b = c$.

System of Equations: A collection of two or more equations with the same set of variables.

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