Solving Equations Using Graphing and Substitution
Name___________________________________________
Date____________________________
This activity uses Graphing & Substitution (2) applet designed with the open educational resource
GeoGebra. The applet illustrates a method of solving equations by graphing, tracing, and substitution.
Background:
The applet is designed to model and solve a variety of equations of the form: ax + b = cx+d
In the Graphing & Substitution (2) applet, the default equation that is loaded is: x+2 = 3x+4
The task is to find a solution for the variable x that will make the expression on the left side of the
equation equivalent to the expression on the right side of the equation.
This can be accomplished by doing the following:
Step 1: Graph the expression on the left side of the equation. [ In this example, graph y = x+2. ]
Step 2: Graph the expression on the right side of the equation. [ In this example, graph y = 3x+4. ]
Step 3: Trace the graph of each expression to find the value(s) of x that are the same for both the
right and left side of the equation. [In this example, when is x+2 giving the same value as 3x+4 ?]
This can be seen in the substitution table. This is also seen in the graph as the point of intersection.]
Use of the Applet
The checkboxes shows and/or hides the graphs of the equations.
The values of x in the equation
can be varied by the use of sliders.
Click on the dot with the selection
arrow and move right or left to
change the value of x in both sides
of the equation.
The equations can be varied by
moving the sliders above
expressions.
Move the slider until you find a value for x that when substituted provides a solution that makes the
right and left side equivalent. In this case the value for x is -1 and you can see this in the ordered pair of
the intersection point.
The value of -1 for x makes both sides of the equation equal values. Notice that when -1 is substituted
for x both sides of the equation equal 1.
Click the checkbox to see the values in a table
Use the Solving Equations Using the Trace Method (2) applet to solve the following equations:
Predict the solution using the graph. Solve for x. Check your solution with the tool. Record
all the steps of the solution.
1. 2x + 4 = 3x + 4
2. x -1 = -x + 5
3. -x + 4 = -2x + 3
4. 2x – 5 = -x + 4