Coordinate Algebra - Introduction to the TI-83 plus Graphing Calculator

Activity: Solving a system of linear equations

Standard: Solve systems of equations

MCC9‐12.A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Represent and solve equations and inequalities graphically

MCC9‐12.A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted

in the coordinate plane, often forming a curve (which could be a line).

MCC9‐12.A.REI.11 Explain why the x‐coordinates of the points where the graphs of the equations y = f(x) and y =

g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using

technology to graph the functions, make tables of values, or find successive approximations. Include cases

where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.


Part A.
1. Press Y =. Type in Y1 = 2x + 1 and Y2 = x – 2.
2. In order to graph in a standard screen, press ZOOM and select 6: ZStandard. (This is from -10 to 10 in the WINDOW

3. Press TRACE .You will be tracing on the function Y1, as indicated in the top left corner of the screen. Use the left and right arrow keys to move the cursor to the point where the two lines appear to intersect.

4. You will notice that there are several decimal places with the coordinates. To have it limited to 0.1, press MODE. Move the down arrow to highlight Float and move the cursor to highlight 1 and press ENTER.

5. Press TRACE and begin to follow the line Y1 towards the intersection point. Press. This will move your cursor to trace on the function Y2. Press the again. Are the X = and Y = the same

numbers? ______If not, what is the difference? ______

Part B.

1. To get a more exact answer, let’s look at a table of values.

Press 2nd WINDOW TBLSET. Match the settings at the right.

2. Press 2nd GRAPH TABLE. Examine the table. Arrow up

or down to find the x-value that gives the same y-value for both

functions. What is the x-value? ______The y-value? ______

Part C.

Clear out your Y1 and Y2 and use your calculator to find the solution to this problem:

a. What equations will you enter as Y1 = ______and Y2 = ______?

b. Solve the system x = ______and y = ______.

c. Interpret the solution of the system in terms of the problem situation.

______

d. Which calculator method did you use to solve this system? ______

Another method:

1. Return to the graph. Press 2nd TRACE CALC. Press 5: intersect to find the exact solution.

2. Use the arrow keys to move the cursor to
• The first line, Y1, and press ENTER.
• The second line, Y2, and press ENTER.
• The Guess? of the intersection point and press ENTER.
What is the intersection point? ______
Is this the same point you got in parts A - C of this activity?______

For more activities, please see the Texas Instruments website at:

http://education.ti.com/calculators/downloads/us/Activities