The System Solver was developed to support you and your students' understanding of systems of linear equations. The System Solver offers users the unique opportunity to perform operations on a system and immediately observe the graphic, tabular, and symbolic results of the procedure at each step. Using the System Solver, you can:
Getting to Know the System Entry Interface
Entering a System
The Main System Solver Interface
Working with the Graph Window
Working with the Coordinate Table
Performing an Operation on Both Sides of the System
Deleting and Starting Over
The About Button
When you start the System Solver, the first screen is the system entry interface shown below. The interface contains two equation entry dialog boxes. This is the place where you select your equation form and enter the equations for the system you wish to solve. Each of these areas is explained in detail in this guide.
System Entry Interface
As you go through this material, it's convenient to open the System Solver in a separate window so that you can work with the tool while following the instructions. Click System Solver to launch the interactive. When the System Solver launches, you will see the default values shown above.
Note If you click the Start Solving button immediately, before entering values, you will get a message indicating that the system that you have submitted is a dependent system. If at any time you find you have entered a system that gives you an error message, you can click on the Start Over button to return to the system entry interface (see Deleting and Starting Over below).
In order to show you how the System Solver works, you'll be guided through a typical system solution that demonstrates the functionality of each part of the System Solver. Start with the following system.
Note Although the illustrations and examples are shown in the dialog labeled Equation 1, the operation is identical for Equation 2.
Equation Entry Dialog Box
Equation Format Selections
Equation Entry Dialog Boxes
Now that you have entered a system and clicked on the Start Solving button, the System Solver presents the main interface. Take a moment to note each part of the interface.
Main System Solver Interface
The main Graph Window contains a Cartesian plane showing a gray line on the x-axis and the y-axis for each equation in your system. There are also tools that allow you to modify the display. At the top of the screen are the Zoom buttons.
As shown below, when you zoom out, you see a larger area of the plane. A blue and a red dot correspond to the colors of the equations below the Graph Window. The red dot is on the line represented by Equation 1. The blue dot is on the line that represents Equation 2. In this example, they share a common x-coordinate.
A Shared x-Coordinate in the Graph Window
In the Coordinate Table (see below), you can see the shared x-coordinate is −6.
Note Scroll across the Graph Window by moving your cursor over the window until the cursor changes its shape to a hand. Then, click and hold while moving the Graph Window to reveal additional area.
Below the Graph Window is the Tabular Area of the interface.This is where your two current system equations are displayed in the Symbolic Representation area. There is also a Coordinate Table with a row of numbers and a Slider Bar for displaying more values. The row of numbers represents the coordinates of the red and blue indicators in the Graph Window.
The traditional way to find the intersection of a system is through algebraic operations. The System Solver allows you to perform an operation on both sides of an equation within a system, using dialog boxes.
Operation Selection Buttons
Term Operations Dialog Box
Result of First Operation
Next, you will perform a function operation on the selected system, substituting Equation 3 into Equation 2.
Operation Selection Buttons
This brings up the Function Operations Dialog.
Function Operations Dialog
Note that as you do so, the results in the Real Time Results section change to show how your operation will be reflected in a new equation, Equation 4.
Function Operations Selections
Note that when you choose Substitute, the new Equation 4, in the Real Time Results area, changes to reflect the result of the operation.
Result of Second Operation
System Display Area Showing Solved System
You have solved the system and found that the coordinates of (y = −4) and (x = 18) are the intersection point of the system.
The last two buttons of interest in the Symbolic Representation Area are the Undo button and the Start Over button.
Undo Button and Start Over Button
Note You can't delete your initial system using the Undo button. If you wish to delete that system, use the Start Over button instead.
The About Button
Clicking on the About button brings up the About the System Solver pop-up. You can view the version number of the System Solver you are running, as well as find Credits and Acknowledgements. The version number can be very helpful if you need to ask for Technical Support or run into unexpected operational issues.
The About the System Solver Pop-up