What is a system of equations?

A system of equations consists of two or more equations that share common variables, which are solved simultaneously. This means you are looking for a solution set that satisfies all equations in the system at once. For example, if you have two equations in two variables, the solution represents the point where the graphs of these equations intersect on a coordinate plane.

This understanding is critical in various applications, including solving problems in algebra, economics, and engineering, where multiple conditions must be met at the same time. Systems of equations can be linear or nonlinear and can employ methods such as substitution, elimination, or graphical approaches to find solutions.

The other options do not capture the essence of a system of equations. A single equation with multiple variables refers to just one equation, not a system of multiple equations. An inequality involving two variables does not fit the definition as it does not involve simultaneous satisfaction of equations. Finally, a method for calculating slopes pertains to a different mathematical concept that relates to the characteristics of linear equations rather than a system of equations itself.