Grade 67 Simultaneous Equations Solve two linear simultaneous

Grade 6/7 Simultaneous Equations Solve two linear simultaneous equations in two variables algebraically and graphically If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Lesson Plan Lesson Overview Objective(s) Solve two linear simultaneous equations in two variables algebraically and graphically Grade Prior Knowledge Rearranging equations Substitution Solving equations Duration Provided prior knowledge of basic algebraic skills are secure this content can be taught with practice time within 60 minutes. Resources Print slides: 4, 10, 12, 16 6/7 Equipment Progression of Learning What are the students learning? How are the students learning? (Activities & Differentiation) Simultaneous equations have solutions where their lines intersect Give students slide 4 printed. Show slide 5 and 6 to illustrate where solutions to equations exist. Students to state solutions for x – y = 4 and x + 2 y = 2. 5 Simultaneous equations can be solved using the method of elimination. Demonstration the method of elimination using slide 7. Allow students to copy down each step and to then attempt to replicate this method for the 2 nd example on their sheet (x - y = 2 and 4 x + 3 y = 29). Discuss why this method is called elimination (either the x or y is removed through +/- the equations – provided the one of the coefficients are the same). 15 Simultaneous equations can be solved using the method of substitution. Guide students through the substitution example on their sheet using slide 9. Discuss how this varies from the elimination method. Students to complete another example independently. Give students slide 10 printed. Students to work on independently using either method. Review answers. 20 Solving two linear simultaneous equations in two variables algebraically in contextualised problems Give students slide 12. Allow students to attempt question on their own for 2 minutes. Review question together and model answer. Stress the importance of making a conclusion. 10 Solving two linear simultaneous equations in two variables algebraically in exam questions (from specimen papers) Give students slide 16. This includes 2 exam questions related to objective. Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme to show the marks are allocated. 10 Next Steps Assessment Quadratic Simultaneous Equations PLC/Reformed Specification/Target 6/Algebra/Simultaneous Equations (Linear)

Key Vocabulary Variables Substitution Elimination Algebraic Graphic Rearranging Unknown

Simultaneous Equations x-y=4 x + 2 y=2 x - y = 2 4 x + 3 y = 29 x=y+6 x + y = 14 Student Sheet 1 Elimination Substitution 5 x + y = 22 x + y = 9 2 x - y = 6 3 x+1 = y

How to solve simultaneous equations graphically x-y=4 When x=4, y=0 When x=0, y=4 and so forth This can be seen graphically where solutions exist all along the line.

How to solve simultaneous equations graphically The same is true for x + 2 y = 2 When x=0, y=1 When x=2, y=0 and so forth We can find the solutions for x-y=4 and x + 2 y=2 simultaneously by looking at the intersection of the graphs. You will see there is exactly one solution. This occurs at x=3 ⅓ and y=-⅔

How to solve simultaneous equations ELIMINATION 5 x + y = 22 Step 1: Add Step 2: Solve for x 2 x - y = 6 7 x = 28 x = 4 Step 3: Substitute Step 4: Check by substituting both values into other equation 5 x 4 + y = 22 20 + y = 22 -20 y =2 Add If the y co-efficients were both positive or negative – then we would SUBTRACT the equations

How to solve simultaneous equations ELIMIINATION x - y = 2 Step 1: Balance coefficients Step 2: Solve for x by adding Step 3: Substitute x to find y 4 x + 3 y = 29 3 x - 3 y = 6 4 x + 3 y = 29 7 x = 35 x = 5 4 x 5 + 3 y = 29 20 + 3 y = 29 -20 Step 4: Check by substituting both values into other equation -20 3 y = 9 y = 3 (2) (2)

How to solve simultaneous equations - SUBSTITUTION Step 1: Sub equation 2 into equation 1 for y. Step 2: Simplify the equation and solve for x Step 3: Substitute x to find y Step 4: Check by substituting both values into other equation x + y = 9 3 x+1 = y x + (3 x+1) = 9 4 x + 1 = 9 4 x = 8 x = 2 x + y =9 2+ y =9 -2 -2 y = 7 (1) (2) (1) x 3 (2) x=y+6 x + y = 14 x=10, y=4

Practice 4 x +2 y =44 3 x +2 y = 36 3 x – y = 4 4 x – 4 y=0 2 x + y =8 5 x – 3 y =31 3 y +5 x =47 y= 3 x -17 x = 5 y– 15 4 x + y = 45 Student Sheet 2

Practice 4 x +2 y =44 3 x +2 y = 36 x=8, y=6 3 x – y = 4 4 x – 4 y=0 x=2, y=2 2 x + y =8 5 x – 3 y =31 x=5, y=-2 3 y +5 x =47 y= 3 x -17 x=7, y=4 x = 5 y– 15 4 x + y = 45 x=10, y=5

Problem Solving and Reasoning Three chews and four bubblies cost 72 p. Five chews and two bubblies cost 64 p. How much does one chew and one bubbly cost? • If no solutions exist – what does the graph look like? • Spot the mistake: 2 x + 6 y = 8 (1) x + 3 = y (2) 2(x+3) + 6 y = 8 • When should you use substitution and when should you use elimination? Justify Student Sheet 3

Problem Solving and Reasoning Three chews and four bubblies cost 72 p. Five chews and two bubblies cost 64 p. How much does one chew and one bubbly cost? Form a simultaneous equation – Use c for chew and b for bubblies: 3 c + 4 b =72 5 c + 2 b =64

Problem Solving and Reasoning Step 1: Balance coefficients Step 2: Solve for x by subtracting (2)(1) Step 3: Substitute c to find b Step 4: Check by substituting both values into other equation 3 c + 4 b = 72 5 c + 2 b = 64 3 c + 4 b= 72 10 c + 4 b = 128 7 c = 56 c = 8 p 3 x 8 + 4 b = 72 24 + 4 b = 72 -24 4 b = 48 b = 12 p (1) (2) x 2 (2)

Reason and explain If no solutions exist – what does the graph look like? Spot the mistake: 2 x + 6 y = 8 (1) x + 3 = y (2) 2(x+3) + 6 y = 8 When should you use substitution and when should you use elimination? Justify

Exam Question – Specimen Papers Student Sheet 4

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers

Exam Question – Specimen Papers Student Sheet 4

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers