System Solver: Warm-Up

It's always a good idea to "warm up" or acquaint yourself with a new software tool before using it with an activity. If you feel comfortable exploring the buttons and features on your own, feel free to do that. If you prefer a more structured exploration, try the activities below.

Click to open the System Solver.

Note The System Solver opens in a new browser window. As you explore the software, keep this window open for reference.

As you navigate through the System Solver's screens and dialog boxes, familiarize yourself with the elements of each. How many buttons are there? What guesses can you make about what they do? What other controls or data entry fields are on the screen?

Warm-Up A: Entering the system

In the following tasks, you will enter the system Two equations in a system. Equation 1 is y -5 = -x + 9. Equation 2 is 3 over 2 x + 3y = 15

When you open the System Solver, a window for entering the system you want to solve is displayed. Note how there are two areas of the screen where you can enter an equation in the system. You'll see how to use different equation formats. You must enter coefficients and constants as fractions, so remember to set the denominator as well as the numerator.

A dialog box for entering two equations in different mathematical formats.

In order to enter this system, you'll need to choose a different equation format than  y = Mx + B, which is the default equation format. You'll also input the values for coefficients and constants in the system.

  1. Under Equation 1, click on the default equation format ( y = Mx + B) to display the other formats.

    These formats allow you to enter most systems you're likely to encounter.

  2. Select the appropriate format for Equation 1.
  3. Click the down arrows A button with an arrow pointing down next to any coefficient or constant to select a value from the menu. (The down arrow A button with an arrow pointing down button always indicates a selectable menu.)

  4. Enter the coefficients and constants to complete Equation 1.
  5. Follow the same steps for entering Equation 2.

  6. Check your entries for the system and click Start Solving.

After you click Start Solving, the display where you've been entering the system is replaced by another screen, on which you can solve the system, and view it in symbolic, graphic, and tabular formats.

Warm-Up B: Exploring the Solver

Before performing any operations to solve the system—you'll do that shortly—take some time to explore this new screen.

  1. Find the three main areas of the screen: symbolic, graphic, and tabular.

  2. Click and drag on the graph to display the point where the two lines intersect.

  3. Move the slider bar that is on the right side of the tabular area by clicking or dragging.

Warm-Up C: Solving the System

Using the System Solver is not the fastest way to solve a system of linear equations. That's because it was designed to slow down the process so you can focus your attention on the intermediate steps.

  1. Click Operate on Both Sides.

  2. For this step, do not enter any values or click Accept until instructed to do so in Step 3. Explore the Operation area of this dialog box to determine what operations you can perform on the equation. The down arrow A button with an arrow pointing down button indicates a selectable menu.

  3. Now, add 5 to both sides of Equation 1 and click Accept.

  4. Before you continue solving the system, check out what happens when you move the slider bar to the right of the tabular area all the way down and up again.

  5. Click Combine Equations.
  6. When the Combine Equations dialog box appears, select Substitute from the pull-down menu.
  7. Click on the equations, which will display a pull-down menu, so that Equation 3 is substituted into Equation 2.

    The Function Operations window for operating on the equations.

  8. Click Accept and the main window will reappear

    A window displays the history of the solution process as progressive pairs of systems.

  9. Move the slider bar to the right of the tabular area down and up again.

  10. Continue solving the system until you are comfortable using the System Solver.