Lesson: Solving Systems of Equations using Substitution Method

Standard: 8.F.3 - Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.

Objective: By the end of this lesson, students will be able to solve systems of equations using the substitution method.

Materials: - Whiteboard or chart paper - Markers - Worksheets with sample problems (see below) - Graph paper - Calculators (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 them 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.
   • Emphasize that the goal is to find the values of the variables that make both equations true simultaneously.
2. Explanation and Example (10 minutes):
   • Write the following system of equations on the board: Equation 1: 2x + y = 7 Equation 2: 3x - 2y = 4
   • Explain that we will solve this system using the substitution method.
   • Ask students to choose one equation to solve for one variable. Let’s choose Equation 1 and solve for y.
   • Show the steps: 2x + y = 7 y = 7 - 2x
   • Explain that we now have an expression for y in terms of x.
   • Substitute this expression for y in Equation 2: 3x - 2(7 - 2x) = 4
   • Solve for x: 3x - 14 + 4x = 4 7x - 14 = 4 7x = 18 x = 18/7
   • Substitute the value of x back into Equation 1 to find y: 2(18/7) + y = 7 36/7 + y = 7 y = 7 - 36/7 y = 49/7 - 36/7 y = 13/7
   • Therefore, the solution to the system of equations is x = 18/7 and y = 13/7.
3. Guided Practice (15 minutes):
   • Distribute worksheets with sample problems to each student.
   • Instruct students to solve the systems of equations using the substitution method.
   • Circulate around the classroom to provide assistance and answer any questions.
   • After students have completed the problems, review the solutions together as a class.
4. Independent Practice (15 minutes):
   • Provide additional practice problems for students to solve independently.
   • Encourage them to use graph paper to graph the equations and estimate the solutions.
   • Students can use calculators to check their solutions if desired.
   • Collect the completed worksheets for assessment purposes.
5. Conclusion (5 minutes):
   • Recap the steps involved in solving systems of equations using the substitution method.
   • Emphasize the importance of checking solutions by substituting them back into the original equations.
   • Answer any remaining questions and address any misconceptions.

Sample Problems for Guided and Independent Practice:

1. Solve the following system of equations using the substitution method: Equation 1: 3x + 2y = 10 Equation 2: 2x - y = 5

2. Solve the following system of equations using the substitution method: Equation 1: 4x - 3y = 8 Equation 2: 2x + y = 5

3. Solve the following system of equations using the substitution method: Equation 1: 5x + 3y = 17 Equation 2: 3x - 2y = 4

4. Solve the following system of equations using the substitution method: Equation 1: 2x + 3y = 11 Equation 2: 4x - y = 7

Note: The sample problems can be modified or expanded based on the needs and abilities of the students.