How to Solve Simultaneous Equations With a Graphing Calculator

Simultaneous equations contain two or more unknown quantities and are related to one another. For any set of equations, there can be only one unique combination of values that can satisfy the equations. To solve simultaneous equations you use substitution, elimination or the graphing methods. These methods are long and tedious but using a graphing calculator can make the task easier.

Difficulty:

Moderate

Instructions

Things You'll Need

• TI 83 Plus graphing calculator

Graph the Equations

1. Choose the equations you need to solve. As an example, use Y1= X+3 and Y2= 5X - 2.

2. Make sure that the equations are in the form Y= AX + B.

3. Turn on the calculator and press the "Y= " key. You see a list of Y values (Y1 to Y7).

4. Input the equation for Y1 by pressing the "X,T, θ, n" key, then "+ 3." Hit the "ENTER" key when done.

5. Follow with the equation for Y2. Input "5," press the "X,T, θ, n" key, then input "- 2." Press the "ENTER" key again.

6. Press the "ZOOM 6" function key to see the graph. Note that when you do not see the graph on the screen window then you must set appropriate axes. You set the axes by pressing the "WINDOW" key and setting values for "XMIN," "XMAX," "YMIN" and "YMAX" and then hit the "GRAPH" key.

Find the Intersection Point of the Equations

1. Find the intersection by pressing "2nd" and "TRACE 5" function keys. The result is a graph of two intersecting lines. Now locate the coordinates of the intersection point.

2. Select a point on the first line by using the arrow keys then hit "ENTER." The coordinates X,Y for this line appear on the screen.

3. Choose a point on the second line in the same manner as in Step 2 then press "ENTER." Make sure that the cursor is on the second line before hitting "ENTER." You get X,Y coordinates for this line and then the calculator asks for a guess of the intersection point.

4. Estimate the intersection by using the left or right arrow keys. Choose a location near the intersection point shown on the screen then select the "ENTER" key again. It displays the coordinates of your guess.

5. Hit the "ENTER" key one last time and the intersection point of X=1.25, Y= 4.25 is the solution for these equations.

6. Check the results by substituting X and Y values into the equations.

Tips & Warnings

• The instructions given here are for a TI83 Plus calculator (see Resources to learn about some other models).

• Make sure that the equations inputted for the two equations are of the form Y= AX + B because this is the form used by the calculator to input the equations.

• Remember to set suitable "XMIN," "XMAX," "YMIN" and "YMAX" axes.