1. Simultaneous Equations
Grade 6/7
Simultaneous Equations
Solve two linear simultaneous equations in two variables algebraically and graphically
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Solve two linear simultaneous equations in two variables algebraically and graphically
Grade
6/7
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
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 + 2y = 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 2nd example on their sheet (x - y = 2 and 4x + 3y = 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 how the marks are allocated.
Next Steps
Quadratic Simultaneous Equations
Assessment
PLC/Reformed Specification/Target 6/Algebra/Simultaneous Equations (Linear)

3. Key Vocabulary
Variables Substitution Elimination Algebraic Graphic Rearranging Unknown

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

5. 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.

6. How to solve simultaneous equations graphically
The same is true for
x + 2y = 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 + 2y=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

7. How to solve simultaneous equations ELIMINATION
5x + y = 22
Add
2x - y = 6
Step 1: Add
7x = 28
Step 2: Solve for x
If the y
co-efficients were both positive or negative – then we would SUBTRACT the equations
x = 4
Step 3: Substitute
5x4 + y = 22
20 + y = 22
-20
-20
Step 4: Check by substituting both values into other equation
y = 2

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

9. How to solve simultaneous equations - SUBSTITUTION
x + y = 9
(1)
3x+1 = y
Step 1: Sub equation 2 into equation 1 for y.
(2)
x + (3x+1) = 9
(1) x3
4x = 9
(2)
4x = 8
Step 2: Simplify the equation and solve for x
x = 2
x + y =9
Step 3: Substitute x to find y
(2)
2 + y = 9
Step 4: Check by substituting both values into other equation -2 -2
y = 7
x = y + 6 x + y = 14
x=10, y=4

10. Practice 4x +2y =44 3x +2y = 36 3x – y = 4 4x – 4y=0 2x + y =8
Student Sheet 2

11. Practice x=8, y=6 x=2, y=2 x=5, y=-2 x=7, y=4 x=10, y=5 4x +2y =44

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

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

14. Problem Solving and Reasoning
3c + 4b = 72
(1)
5c + 2b = 64
(2)
3c + 4b= 72
Step 1: Balance coefficients
(1)
10c + 4b = 128
(2) x2
7c = 56
Step 2: Solve for x by subtracting (2)-(1)
c = 8p
3x b = 72
Step 3: Substitute c to find b
(2)
b = 72
Step 4: Check by substituting both values into other equation
-24
-24
4b = 48
b = 12p

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

16. Exam Question – Specimen Papers
Student Sheet 4

17. Exam Questions – Specimen Papers

18. Exam Questions – Specimen Papers

19. Exam Questions – Specimen Papers

20. Exam Question – Specimen Papers
Student Sheet 4

21. Exam Questions – Specimen Papers

22. Exam Questions – Specimen Papers

23. Exam Questions – Specimen Papers