Definition

Noun: A set of two or more equations that contain two or more variables. The goal is to find values for the variables that satisfy all the equations in the set at the same time (simultaneously).

Usage

This term is used primarily in mathematics, specifically in algebra. It describes a problem where multiple conditions (equations) must be true together. The solution is the set of variable values that makes every equation true concurrently.

Examples

• In the system of simultaneous equations and , the solution is and .
• Solving a pair of simultaneous equations often involves methods like substitution or elimination.
• The real-world problem was modeled using a set of three simultaneous equations.

Advanced Usage

• Conceptual Use: The term can be used metaphorically outside of strict mathematics to describe a situation where multiple, interdependent conditions must be met at once.
  • Balancing the budget was like solving a set of simultaneous equations involving revenue, expenses, and economic forecasts.

Variants and Related Words

• System of equations: A more general synonym for "simultaneous equations."
• Linear equations: A common type of equation found in systems of simultaneous equations (e.g., ).
• Simultaneous (adj.): Happening, existing, or done at the same time. This is the root adjective from which the term is derived.

Synonyms

• System of equations
• Set of equations

Related Phrases

• Solve simultaneous equations: The standard phrase for finding the solution.
• Simultaneous linear equations: A specific and very common type of simultaneous equation.

Noun

1. a set of equations in two or more variables for which there are values that can satisfy all the equations simultaneously