Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What method can be used for solving systems of equations graphically?

1. Using substitution to find variable values

2. Plotting the equations on the same graph and finding the intersection point

3. Employing the quadratic formula to analyze results

4. Using matrix operations to solve

The correct answer is: Plotting the equations on the same graph and finding the intersection point

The method for solving systems of equations graphically involves plotting each equation on the same coordinate plane and identifying the point where they intersect. This intersection point represents the values of the variables that satisfy both equations simultaneously. Graphing provides a visual representation of the equations, making it easier to understand how they relate to each other and to identify the solution directly. When two lines intersect, the coordinates of that intersection give the solution to the system of equations. If the lines do not intersect, it indicates that there may be no solution (the lines are parallel), and if they overlap, it suggests there are infinitely many solutions (the lines are coincident). The other methods listed, such as substitution, the quadratic formula, and matrix operations, involve algebraic manipulation rather than graphical representation, making them distinct approaches to solving systems of equations. While these methods are valid and useful in their own contexts, they do not apply to the graphical solution of systems of equations. Thus, plotting the equations and finding their intersection is the correct approach for solving systems graphically.