Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What does the graphing method of solving equations entail?

1. Finding a common multiple

2. Graphing the system of equations and identifying the intersecting point

3. Substituting values into equations to find a solution

4. Determining the area under the curves

The correct answer is: Graphing the system of equations and identifying the intersecting point

The graphing method of solving equations involves visualizing the equations on a coordinate plane to find their points of intersection. By graphing each equation, the solutions to the system are represented as points where the graphs intersect. This method is particularly useful for providing a clear visual representation of the relationships between the equations and helps identify whether there are one, none, or infinitely many solutions based on the nature of the lines or curves. When the graphs of the equations intersect at a single point, that point has coordinates that satisfy all the equations in the system—hence it is the solution to the system. If the lines are parallel, they will never intersect, indicating that there is no solution. If they overlap, it means there are infinitely many solutions along the entire line. Utilizing this graphical approach allows for a more intuitive understanding of the solutions to the equations compared to algebraic methods, which might not provide as immediate of a visual cue regarding the nature of the relationships involved. This visualization aspect is the core reason why identifying the intersecting point effectively represents the solution to the equation.