Solving Graphic Equations with the Intersection Method & a Graphing Calculator
Lesson Overview
In this lesson, students will be introduced to the substitution method to solve systems of equations algebraically, as well as using the intersection method on the graphing calculator.
Student Objectives
In this lesson, students will:
 Review solving quadratic formulas algebraically
 Learn the substitution method to solve a system of equations
 Learn the intersection method with the graphing calculator to solve a system of equations
 Listen to the teacher give a lecture on these two concepts, and asking questions when appropriate
 Execute sample problems supplied by the teacher and share their answers orally with the rest of the class
 Learn the following new vocabulary words: system of equations, substitution method, intersection method
Learning Activities

Begin the lesson by giving students a brief overview of what they will be learning (solving systems of equations using the substitution method and the intersection method), and explain that the substitution method is an algebraic method and the intersection method is a graphing method.

Next, explain the substitution method using a simple pair of equations: x2 + y = 0 and 5x = y + 14. Use this process:
 Take the first equation and subtract x from both sides. This will give the following equation: y = x.
 Take the second equation and subtract 14 from both sides. This will give the following equation: y = 5x  14.
 Point out to the students that y is equal to both xand 5x  14, which gives the equation x = 5x  14. This is substitution.
 Add x to both sides, resulting in x + 5x  14, which can be solved algebraically: (x+7)*(x2), with x = 7 and 2. When x = 7, y = 49, and when x = 2, y = 4. The answer can be expressed as ordered pairs: (7, 49), (2, 4).
 Show how these equations can be solved using the intersection finder on the graphing calculator, using this process:
 Turn on the calculator and press the [Y=] key
 Enter the first equation (y = x) on the first line
 Enter the second equation (y = 5x  14) on the second line
 Press the [GRAPH] button to see the graphs (a parabola and a line) on the screen. Adjust the viewing window as necessary so the points at which the two graphs intersect can be seen easily.
 To find the points of intersection: Press [2nd] [TRACE] then 5 to choose “intersect”
 Press the arrow key to move the cursor close to one intersection point and press [ENTER] to select the parabola
 Press the arrow key along the line to move the cursor close to the same intersection point and press [ENTER] to select the line
 Press [ENTER] a third time to have the calculator guess the intersection. Repeat this process with the second intersection point between the parabola and the line.
 Provide students with increasingly difficult examples, which the students will be required to solve as the lecture progresses, and provide their answers orally.
This post is part of the series: Learning About Graphs
This series of lesson plans outline ways to teach students topics pertaining to solving algebraic equations using graphs and graphing calculators.