College Algebra

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Solution set

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College Algebra

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.

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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?
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