Alternate Method to Solve a System of Equations by Substitution

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SWBAT solve a system of equations by substitution.

Big Idea

Students review the steps of solving a system of equations by substitution by alternating steps as they solve problems in pairs or groups.

Warm up

10 minutes

I plan this Practice warm-up as a follow up from the previous day's lesson to have students successfully use the Substitution Method to solve a system of equations during this lesson.  When using Substitution, the first step is often: solve one of the equations for one of the variables (in terms of the other).  This warm-up is meant to clarify the meaning of "solving an equation in terms of x" or "solving an equation in terms of y." This skill is difficult for students, and one difficulty is understanding the meaning of the instruction, "solve for."    


Materials needed for this lesson:

  • Copies of the Practice Worksheet or work off of the projector on their own paper.
  • Copy of guided notes to complete and place in note book.
  • Individual white boards, eraser, or marker (a piece of paper may be used instead)


Guided Notes

10 minutes

The objective of this lesson is for students to review how to solve a system of equations by substitution from the previous day's lesson. During the guided notes, I remind the students that substitution can be used to solve any system of equations. I also inform students that the method is easier to use when at least one of the equations has a variable with a coefficient of 1 or -1.  

I use the Guided Notes to review the vocabulary and procedures used to solve a system of equations by substitution.  I discuss reasoning with the students for each of these steps as I work through the guided notes with them.  In the first part of the guided notes, students recognize when to use substitution, and practice identifying the variable with a coefficient of 1 or -1 in front of it. In the second part of the guided notes, I provide an example to work through the steps, and verbally state the reasoning aloud as I work the problem.  I demonstrate the steps for substitution and the reasoning in the video below.



Cooperative Activity

20 minutes

I form the cooperative groups for this segment of the lesson by counting students off by three's. Pairs of students may also be used if necessary.  Each group sits together at a table. There are tables in my classroom instead of desk that work well for cooperative learning.

After the groups are seated, I provide each group with an individual white board, eraser, and marker.  I instruct the students in each group that the white board is passed in order from student to student until the problem is solved.  Each student works one step of the problem and passes it to the next student.  When passing the board to the next student, the student explains the step performed and why. For example, " I solved for x in the second equation because it has a coefficient of 1."  The next student works another step and passes it to the other student or partner and states the step performed and why.  This rotation continues until the problem is solved.  If I judge that some students work slower than the other groups, I will check each group individually. Students may also raise their hand for assistance if the group comes to a standstill, and no members of the group knows the next step.  At this point, I provide questioning to move the group forward.  Students must persevere(Math Practice 1), and continue until a solution is found.

After a group completes a problem, I provide them with the next problem to work.  The problems that I provide in the cooperative group activity are the 6 problems that are in the guided notes.  The next problem will begin where the group left off. Do not start the board over with student 1.  

I have the Key in hand to check solutions quickly, and the problems to allow students to move to the next problem.

When students complete the 6 problems, each student is to complete the exit slip.  Groups that do not complete all six problems in the cooperative activity, continue to work until the end of the period with the teacher facilitating the remaining groups.  These students will complete the exit slip as homework.  

Exit Slip

10 minutes

I use the Exit Slip as a formative assessment to check for student understanding after working with solving a system of equations by Substitution for two lessons.  When assessing the exit slips, I will be looking for student comprehension of the following:

  • Even though 2x + 3 does not look like y in the first equation, the expressions are equivalent.
  • Substitution means to replace the variable.
  • When using the distributive property, the number needs to multiply times both terms.
  • Zero is a solution for x, and y must be found, it does not represent no solution.  It means the 2 lines are going to intersect at one point, which should be reinforced when graphing the system in problem 2.

If students are still struggling after this lesson, I will provide a Retake of the exit slip along with resource videos on solving a system of equations by Substitution.