FTCE General Knowledge Math Practice Test

What defines the solution set of linear equations?

1. Three different variables

2. Unordered points on a graph

3. All ordered pairs satisfying both equations

4. A single solution

The correct answer is: All ordered pairs satisfying both equations

The solution set of linear equations is defined as the collection of all ordered pairs that satisfy both equations simultaneously. In the context of a two-variable system, this means that any point (x, y) that makes both equations true is included in the solution set. When you graph the linear equations, the solution set corresponds to the intersection points of the lines represented by the equations. If the lines intersect at one point, that point is the single solution. If they coincide, then the solution set consists of infinitely many points along the line. If they are parallel and do not intersect, the solution set is empty. Therefore, understanding that the solution set encompasses all pairs that meet the criteria of satisfying both equations is fundamental in analyzing linear systems. Consequently, the correct choice highlights the comprehensive nature of ordered pairs that satisfy the equations rather than just focusing on specific scenarios or characteristics like the number of variables or points on a graph.