Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is a solution of a system of linear equations?

1. Any ordered pair that satisfies one equation

2. Any ordered pair in a system that makes all the equations true

3. The intersection point of any two lines

4. The numerical value of the variables in one equation

The correct answer is: Any ordered pair in a system that makes all the equations true

A solution of a system of linear equations refers specifically to any ordered pair that makes all the equations in that system true simultaneously. In the context of linear equations, each equation represents a line, and the solution represents the point or points at which these lines intersect. When considering multiple equations in a system, it is essential that the ordered pair satisfies every individual equation. For example, if a system consists of two equations, both equations must hold true for the ordered pair to be considered a valid solution to the system. Thus, option B accurately captures this concept, as it specifies that the ordered pair must satisfy all equations within the system. In contrast, other options describe aspects that do not fully encompass the definition of a solution for a system. For instance, the first option suggests that satisfying only one equation is sufficient, which ignores the necessity for all equations to be satisfied. The third option refers to the intersection point of two lines, which could be a solution, but does not clarify the need for that point to satisfy all equations in the system. Lastly, the fourth choice defines a numerical value for the variables only in a single equation, failing to address the broader requirement of satisfying multiple equations.