Lesson: Solving Systems of Equations using Substitution Method

Standard: 8F2 - Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.

Objective: Students will be able to solve systems of equations using the substitution method.

Materials: - Whiteboard or blackboard - Markers or chalk - Handouts with sample problems - Graphing calculator (optional)

Procedure:

1. Introduction (5 minutes):
   • Begin the lesson by explaining to students that today they will learn how to solve systems of equations using the substitution method.
   • Remind students that a system of equations is a set of two or more equations with the same variables.
   • Explain that the substitution method involves solving one equation for one variable and substituting that expression into the other equation.
2. Explanation of the Substitution Method (10 minutes):
   • Write the following system of equations on the board: Equation 1: 2x + y = 7 Equation 2: 3x - y = 1
   • Explain that we will solve this system using the substitution method.
   • Choose one equation to solve for one variable. In this case, let’s solve Equation 1 for y: 2x + y = 7 y = 7 - 2x
   • Now, substitute the expression for y in Equation 2: 3x - (7 - 2x) = 1
   • Simplify and solve for x: 3x - 7 + 2x = 1 5x - 7 = 1 5x = 8 x = 8/5
   • Substitute the value of x back into Equation 1 to find y: 2(8/5) + y = 7 16/5 + y = 7 y = 7 - 16/5 y = 35/5 - 16/5 y = 19/5
3. Guided Practice (15 minutes):
   • Distribute handouts with sample problems to students.
   • Work through a few examples together, guiding students through the steps of the substitution method.
   • Encourage students to check their solutions by substituting the values back into the original equations.
4. Independent Practice (15 minutes):
   • Assign a few practice problems for students to solve independently.
   • Circulate around the classroom to provide assistance and answer any questions.
5. Conclusion (5 minutes):
   • Review the steps of the substitution method and ask students if they have any questions.
   • Summarize the lesson by emphasizing the importance of checking solutions and practicing the method to become proficient.
   • Encourage students to continue practicing solving systems of equations using the substitution method.

Sample Problems: 1. Solve the following system of equations using the substitution method: Equation 1: 3x + 2y = 10 Equation 2: 2x - y = 4

1. Solve the following system of equations using the substitution method: Equation 1: 4x - 3y = 5 Equation 2: 2x + y = 7

2. Solve the following system of equations using the substitution method: Equation 1: 5x + 3y = 12 Equation 2: 2x - y = 1

Note: You can modify the number and complexity of the sample problems based on the proficiency level of your students.