Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 51097
Solving Systems of Equations by Substitution
In this lesson, students will learn how to solve systems of equations using substitution. Students will have the opportunity for small group and whole
class discussion related to using substitution.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Graphing Calculators,
Internet Connection, Basic Calculators, LCD Projector,
Overhead Projector
Instructional Time: 50 Minute(s)
Freely Available: Yes
Keywords: System of equations, substitution, dependent and independent systems, consistent systems,
inconsistent systems, coinciding lines.
Instructional Design Framework(s): Direct Instruction
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Homework on how to Solve each system by substitution.docx
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to solve linear systems of equations using substitution.
Students will be able to compare graphical solutions with the solutions obtained using substitution and recognize that both methods result in the same solutions.
Prior Knowledge: What prior knowledge should students have for this lesson?
1. Students have learned how to solve linear equations for a given variable.
2. Students have learned how to write a linear equation in slope-intercept form.
3. Students have learned how to graph a linear equation with two variables.
Guiding Questions: What are the guiding questions for this lesson?
1. How can I use the property of substitution to solve a system of equations?
2. What are equivalent systems?
3. How do I know if a system has only one unique solution?
4. How do I know if a system has no solutions?
page 1 of 4 5. How do I know if a system has an infinite number of solutions?
Teaching Phase: How will the teacher present the concept or skill to students?
At the start of class, provide the three graphs and systems as described in the Formative Assessment. Give students an opportunity for group discussion and have whole
class discussion as outlined in the Formative Assessment.
Next, put the students into groups of three to discuss and share ideas together.
Present the students with the graph in example #1-and system from the formative assessment. Use the discussion that occurred in the Formative Assessment to
dictate your instruction. If a group correctly identified substitution method, as a method, allow them to explain it to the class. If no group came up with the substitution
method, ask guiding questions [Do you have coefficient =1 for variable in any equation ?, Can you solve the equation for that variable?] that may lead students to
substitution. Choose students to explain the next steps involved in working the problem by asking them to come to the board and share with the class.
What happens if you do not find any variable with a coefficient equal to 1? Are you still be able to solve the system of equation by substitution method? Yes, look to the
following example:
2X+6Y=2
(subtract 6y from each side)
2X=2-6Y
(then divide by 2)
x=1-3y
3X+2Y=10
(substitute x in the second equation)
3(1-3y)+2y=10
(distribute 3 in the parenthesis)
3-9y+2y=10
(combine a like term)
3-7y=10
(subtract 3 from each side)
-7y=7
(divide each side by -7)
y=-1
x=1-3(-1)
substitute y=-1 in the equation x=1-3y
x=4
the solution is (4, -1)
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Next, give the students another problem:
y=-3x+3 and y=2x-7
Give them 5 minutes to work in their groups. Each student should participate in solving the problem by substitution method and try to do it with his/ her partner on
sheet of paper. The teacher should walk around the room and provide any assistance and listen to misconceptions, prompting groups that seem to be having
difficulties. After 5 minutes, ask students to volunteer to work the problem on the board. The teacher may ask the students to check their answers by graph.
The teacher should review the steps of solving the problem by going over it with the class to wrap up all the steps for their notes.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Provide the attached worksheet for students to complete for homework. On the following day before the quiz, go over any questions students may have.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will lead a whole class discussion asking the students to identify the steps necessary to solve systems of equations using substitution. Also, have the
students link the solutions found in substitution with the solutions they identified in the graphs from the Formative Assessment.
Summative Assessment
On the following day administer a quiz:
Solve each system by substitution, check your answers.
1. {x+y=5, x-y=-3}
2. {x-4y=3, 2x-8y=6}
3. {y=2x+3, 2x-y=4}
page 2 of 4 Formative Assessment
Write the following systems and their graphs on the board. Have the students identify the solution of each graph and identify the type of system (independent,
consistent, inconsistent, and coinciding) for each.
Intersecting Lines
Example #1 - Solve the system of equations
Y=-X
Y=X+ 4
Coinciding lines
Example #2
2Y=2X
Y-X=0
Parallel Lines
Example #3
Y=3/2 X +1
Y=3/2X + 3
Independent Systems - have one solution
Inconsistent System / Parallel line - have no solution
Consistent System / Coinciding lines - have infinitely many solutions ( the same line)
Note: The teacher will use the same examples to solve the system of equations algebraically by substitution.
After students have identified the solutions and the types of system. Allow students to take the first example and discuss with their partner any alternative methods.
Have the students share with the whole class their ideas. Acknowledge all ideas presented. If the method is not a correct method, point out to students why the
page 3 of 4 problem cannot be solved in that manner. If a group recognizes substitution, have that group share their work. After taking several suggestions, explain to the
students that today they will be learning how to solve systems of equations using substitution.
Feedback to Students
The teacher will assist students by observing and evaluating understanding, correcting errors, re-teaching and answering questions throughout the lesson.
While the students are working on the similar problems teacher will circulate in the class and give individual assistance to those who need help.
Students are divided into small groups (~3 students) to work together for about 10 minutes
The teacher will walk between groups and check to see if answers are correct on paper
If correct, the teacher will provide positive comments
If incorrect, the teacher will ask leading questions to lead students to understanding.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: ELL: provide extra time, use bilingual dictionary, provide choices, assign a peer tutor, use word walls, and focus on communication by model a
statement for students explaining how you would approach the problems.
ESE: Link topics to prior knowledge, teach technical vocabulary supporting key topics, continually monitor students comprehension.
Reinforce the key ideas.
Ask high level questions, give directions in small distinct steps, use voice intonation to stress points, interject humor, introduce difficult vocabulary and concepts, tell
students what they will learn from the assignment.
Extensions: Teacher will ask the students for challenge question [ 0.02a - 1.5b = 4 & 0.5b - 0.02a = 1.8] to motivate them.
Suggested Technology: Graphing Calculators, Internet Connection, Basic Calculators, LCD Projector, Overhead Projector
Additional Information/Instructions
By Author/Submitter
In this lesson we will use
Make sense of problems and persevere in solving them (MP#1)
Reason abstractly and quantitatively (MP#2)
SOURCE AND ACCESS INFORMATION
Contributed by: Viola Abraham
Name of Author/Source: Viola Abraham
District/Organization of Contributor(s): Orange
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.A-REI.3.6:
Description
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in
two variables.
page 4 of 4