5As Method of Lesson Plan on Ssolving systems of linear equations in two variables by substitution method- detailed
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The document outlines a detailed lesson plan for junior high students on solving systems of linear equations using the substitution method. Objectives include simplifying linear equations and discussing the importance of equality in society, with a focus on student engagement through group activities and step-by-step problem solving. Materials include a PowerPoint presentation and the lesson emphasizes practical application and interventions to promote understanding of linear equations.
5As Method of Lesson Plan on Ssolving systems of linear equations in two variables by substitution method- detailed
- 1. A lesson Plan intended for the demonstration in applying a position Teacher I Solving Systems of Linear Equations in Two Variables by Substitution MethodLesson Plan For Demonstration- Junior High Lesson Plan For Demonstration-Junior High ELTON JOHN BALIGNOT EMBODO Applicant
- 2. I. Objectives: At the end of the lesson, students are expected to: a. simplify linear equations to get the solution sets; b. construct linear equations and solve for the solution sets; c. discuss the importance of equality in the society. II. Subject Matter: Solving Systems of Linear Equations in Two Variables by Substitution Method Reference: Simplified College Algebra page (97) by: Gabino P. Petilos, Ph.D. Skills: analysing and solving Values: equality III. Materials: power point (multimedia presentation), projector, and laptop IV. Procedure: 5A’s Method Teacher’s Activity Students’ Activity A. Awareness a. Review Good morning class! (Checking of attendance) (Checking of assignment) Before we proceed to our next lesson this afternoon. Let us have first a review on our previous topic last meeting. I will give you a very short activity as a sort of review. Directions: Find the equation in solving for x in terms of y and in solving for y in terms of x. For items 1 – 3, find the equation in solving x and for 4 – 5, the equation in solving for y. 1. x + 2y = 8 X = ? 2. 3x + y = 9 X = ? 3. x – y = 5 X = ? 4. 4x + 3y = 7 Y = ? 5. x + 4y = 10 Y = ? (verifying the answers of the students) Do you still have any clarification class? b. Motivation Now class, you have learned already on how to find the equation in solving for the value of one variable (x) in terms of the other variable (y). Good morning Sir! Students do as told 1. x = 8 – 2y 2. x = 9 – y 3 3. x = 5 + y 4. y = 7 – 4x 3 5. y = 10 – x 4 None Sir!
- 3. I have here a pair of equations; x+ y = 6 eq. 1 2x – 3y = 2 eq. 2 Class what does this equal sign mean in this equation x + y = 6? Very good! Another idea? Very good! How could we know that x + y is equal to 6? That is right! By applying your knowledge on our previous topic, we can find the equation for solving x in terms of y which is x = 6 – y and in the same manner, y = 6 – x. Now class, do you know on how to find the value of x having the having the second equation 2x – 3y = 2? In the same manner, do you know on how to find the value of y having the second equation 2x – 3y = 2? Do you know on how to solve for x and for y by substitution method? c. Presentation So be with me this afternoon class as I discuss to you on how to solve systems of linear equations by substitution method. d. Statement of the Aim simplify linear equations to get the solution sets; construct linear equations and solve for the solution sets; discuss the importance of equality in the society. B. Activity I will group you into 5 groups. Each member of the group should cooperate in doing your activity. It means that x + y is equal to 6. It means that the left side of equation is equal to the right side of the equation. We have to find the value of x and the value of y and add them together. No, Sir! No, Sir! No, Sir! Solving Systems of Linear Equations by Substitution
- 4. Directions: On the following pairs of equations, solve for the value of x and for the value of y by following the steps. a.) Solve for one variable (say x) in terms of the other variable (say y) in one of the equations. b.) Substitute the value of the variable (x) found in the first step to the same variable (x) of the second equation. Simplify and solve the resulting equation to find the value of the variable (x). c.) Substitute the value obtained in second step to any of the original equations to find the value of the other variable (y). Group 1 2x + y = -5 eq. 1 2x + 3y = 10 eq. 2 Group 2 2y – x = 5 eq. 1 2y + x = -10 eq. 2 Group 3 x + y = 9 eq. 1 x – y = 5 eq. 1 Group 4 x + 3y = 9 eq. 1 2x – y = -4 eq. Group 5 x – 4y = 1 x + y = -4 C. Analysis Let us now check your solutions and answers. Let us begin checking the solution and answer of the group 1. The first group has this pair of equations; 2x + y = -5 eq. 1 2x + 3y = 10 eq. 2 We have to follow the steps to obtain the correct solutions and answer. What is again the step number 1? Okay! Students do as told Expected answers from the students. x = -25/4 ; y = 15/2 x = -15/2 ; y = -5/4 x = 7 ; y = 2 x = -3/7 ; y = 22/7 x = -3 ; y = -1 The step number 1 states that, “solve for one variable in terms of the other variable of the equations.
- 5. By following the step 1, we can obtain equation for finding y in terms of x for the equation 1, we have y = -5 – 2x . Since we already have this equation for finding y, what is then the next step? Very good! Since we have obtained the value of y in the first equation which is equal to – 5 – 2x or y = -5 – 2x. What will we do to this equation y = -5 – 2x according to the second step? That is right! We have this second equation; 2x + 3y = 10. We will substitute now the value of y in the first equation which is -5 – 2x to the y in the second equation which is 2x + 3y = 10. 2x + 3y = 10 ; y = -5 -2x In this certain equation, what property we can use to simplify the equation? 2x + 3(-5-2x) = 10 Very good! By applying the distributive property, we can obtain; 2x – 15 – 6x = 10 What is then the next thing to do to further simplify the equation? Very good! By combining like terms, we can obtain. -4x – 15 = 10 What shall we now to find the value of x? What property can use? That’s right! Why is there a need to apply the addition property of equality? By applying the addition property of equality in this equation; -4x – 15 = 10 -4x – 15 + 15 = 10+ 15 Substitute the value of the variable found in the first step to the same variable of the second equation. Simplify and solve the resulting equation to find the value of the variable. We will substitute it the y in the second equation. We can use the distribution property of multiplication. We will combine like terms. To solve for x, we will apply the addition property of equality. We need to apply the addition property of equality to remove the -15 in the left side of the equation so that -4x will be isolated.
- 6. The -15 and +15 will be cancelled out since it equivalent to 0. So we now have -4x = 10 + 15 -4x = 25 Finally, what property we can apply to get the value of x? Very good! We have to divide both sides of the equation by negative four to isolate x in the left side of the equation. -4x = 25 -4 -4 x = -25 4 Since, we have already obtained the value of x which is -25/4, how could we find now the value of y? What does the last step state? So we can use either the first equation or the second equation. Let us try to use the first original equation; 2x + y = -5 eq.1 2(-25) + y = -5 4 -25 + y = -5 2 y = -5 + 25 2 y = -10 + 25 2 y = 15 2 Let us use the second equation if we can get the same answer with the first equation. 2x + 3y = 10 2(-25) + 3y = 10 4 -25 + 3y = 10 2 2(3y = 10 + 25 )2 2 6y = 20 + 25 6y = 45 6 6 y = 45 or 15 6 2 To get the value of x, we will apply the division property of equality. We can find the value of y by doing the last step? It states that “Substitute the value obtained in second step to any of the original equations to find the value of the other variable”.
- 7. Since we have already obtained the values of x and y, how could we know then if our answers are correct? Okay, let us try. We will use the first equation. 2x + y = -5 2(-25) + 15 = -5 4 2 -25 + 15 = -5 2 2 -10 = -5 2 -5 = -5 Since, -5 is equal to -5, then our answers are correct. By following the same steps for number 2 to 5. 2. 2y – x = 5 eq. 1 2y + x = -10 eq. 2 2y – x = 5 x = -5y + 2y 2y + x = -10 2y +(-5 + 2y) = -10 4y = -10 + 5 y = -5 4 Second equation 2y – x = 5 2(-5) – x = 5 4 -x = 5 + 5 2 x = -15 2 3. x + y = 9 eq. 1 x – y = 5 eq. 2 x = 9 – y 9 – y – y = 5 -2y = -4 y = 2 x + 2 = 9 x = 9 – 2 x = 7 We will check by substituting the values of x and y in any of the original equation.
- 8. 4. x + 3y = 9 eq. 1 2x – y = -4 eq. 2 x = 9 – 3y 2x – y = -4 2(9 – 3y) – y = -4 18 – 7y = -4 -7y = -22 y = 22 7 x + 3 (22) = 9 7 x + 66 = 9 7 x = -3 7 5. x – 4y = 1 x + y = -4 x = 1 + 4y x + y = -4 1 + 4y + y = -4 5y = -4 – 1 y = -1 x – 4y = 1 x – 4(-1) = 1 x + 4 = 1 x = -3 D. Abstraction In your activity a while ago, you were able to solve the values of x and y. Class if you are going to analyze the steps from first step to last step, what common way you have done to get the values of x and y? So, what do you mean about substitution? Or what substitution is all about? Very good. Yes sir. The common way we have done in getting the values of x and y was substitution. Substitution means that we have to replace the value of a certain variable with the value of the other variable to get its value.
- 9. Values Integration A while ago class, we have discussed about the solving systems of linear equations by substitution. What word can you associate with the word equation? Class, in connection to our real life situation, how are we going to promote equality and prevent inequality? E. Application Activity 1 Directions: Simplify the following pairs of linear equations to get the solution sets by using substitution method. 1. 2x + 2y = 2 eq. 1 2x + 3y = -2 eq. 2 2. x + y = -1 eq. 1 2x + y = -3 eq. 2 3. x – 2y = 1 eq. 1 x + y = 2 eq. 2 4. 3x + y = 8 eq. 1 3x – 2y = 2 eq. 1 5. x + y = 5 eq. 1 2x – y = 1 eq. 2 V. Evaluation Directions: Construct your own five pairs of linear equations using the form ax + by = c, and use the substitution method to solve for the solution sets, the values of x and y. Use ½ sheet of paper. VI. Assignment Directions: Do an advance study about solving linear equations in two variables by using elimination method. We will have a pre- test next meeting. I can associate it with equality sir. I can promote equality and prevent inequality by being fair to everybody in everything that I do. Equality begins with being fair in just a simple action. It begins in us.