1. Simultaneous equations
Starter: Make up a linear equation yourself and give it to your partner to solve
Simultaneous equations

2. Method 1 – Elimination method
Step 1 – Number the
equations
6x + y = 15
4x + y = 11
(1)
(2)
Step 2 – Eliminate one of the unknowns 2x
= 4
Step 3 – Work out the unknown x
= 2
y = 15 x
× 2
Step 4 – Using the value of x in equation 1 or 2 find the value of y.
y = 15 y
= 3

3. Method 1 – Elimination method
Step 1 – Number the
equations
3x + 4y = 17
x + 4y = 3
(1)
(2)
Step 2 – Eliminate one of the unknowns 2x
= 14
Step 3 – Work out the unknown x
= 7
+ 4y = 3 x 7
Step 4 – Using the value of x in equation 1 or 2 find the value of y.
4y = -4 y
= -1

4. Method 1 – Elimination method
Step 1 – Number the
equations
3x +2y = 18
(1)
2x - y = 5
(2)
Step 2 – Balance the coefficient of one of the unknowns 4x
-2y
= 10
(3)
Step 3 – Eliminate unknown by adding 7x
= 28 x
= 4
Step 4 – Using the value of x in equation 1 or 2 find the value of y.
- y = 5 2
× 4 x
y = 5
y = 3

5. Elimination method
How to solve simultaneous equations using the elimination method where both equations need to be changed to obtain the same coefficients in front of the unknown you wish to cancel

6. Elimination method 4x +3y = 27 5x - 2y = 5 8x +6y = 54 = 15 15x - 6y
Step 1 – Number the
equations
4x +3y = 27
(1)
5x - 2y = 5
Step 2 – Balance the coefficients of one of the unknowns in both the equations
(2) 8x
+6y
= 54
(3)
= 15
15x
- 6y
(4)

7. Elimination method 8x + 6y = 54 15x - 6y = 15 23x = 69 x = 3
Step 3 – Eliminate one of the unknowns
(3)
(4)
Step 4 – Work out the unknown
23x
= 69 x
= 3
Step 5 – Using the value of x in equation 1, 2, 3 or 4 find the value of y.
y = 54 x
× 3
y = 54 y
= 5
6y = 30

8. Which ones are you using?
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PLT Skills
Which ones are you using?
Simultaneous Equations
TASK 1) 2) 3) 4) 5) 6) 7) 8) 9)
10)
11)
12) 8

9. Which ones are you using?
Creative Thinker
Effective Participator
Independent Enquirer
Reflective Learner
Self Manager
Team Worker
PLT Skills
Which ones are you using?
Simultaneous Equations
EXTENSION 1) 2) 3) 4) 5) 6) 7) 8) 9)
10)
11)
12) 9

10. 1
3x + 2y = 11
5x – 2y = 13 6
5x - 2y = 0
3x - 2y = -2
x= 3
y = 1
x = 1
y = 2.5 2
a + b = 7
3a – b = 1 7
5a - 4b = -12
2a – 4b = 0
a = -4
b = -2
a = 2
b = 5 3
2x – y = 4
-2x + 3y = -8 8
3x + 2y = -1
4x + 2y = -1
x = 1
y = -2
x = 0
y = -0.5 4
5p + 4q = 13
3p + 4q = 7 9
5x – 3y = 41
4x + 3y = 22
p = 3
q = -0.5
x = 7
y = -2 5
2a + 5b = 11
2a + 7b = 17 10
3p + q = 9
2p + q = 5
p = 4
q = -3
a = -2
b = 3
Pupil print off sheet: End show then file then print and select slide 2
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Answers

11. 1
2a + 3d = 18
3a – 4d = -7 6
3x + 2y = 8
2x + 3y = 2
a = 3
d = 4
x = 4
y = -2 2
2x – 4y = 18
4x + 3y = 14 7
3a + 5b = -4
5a – 2b = -17
a = -3
b = 1
x = 5
y = -2 3
4p – 5q = 41
3p – 4q = 32 8
2x + 3y = -11
-6x + 8y =-35
p = 4
q = -5
x = 0.5
y = -4 4
2x + 3y = 7
3x + 6y = 15 9
8p – 6q = 56
6p + 4q = -9
x = -1
y = 3
p = 2.5
q = -6 5
3a – 8b = -5
5a – 4b = -13 10
2x – 3y = 9
3x + 4y = -29
x = -3
y = -5
a = -3
b = -0.5
Pupil print off sheet: End show then file then print and select slide 3
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Answers

12. Solve the following simultaneous equation:
PLENARY ACTIVITY
Solve the following simultaneous equation:
4x - 3y = 7
x + 3y = 13
Signs different (+) +
5x = 20
x = 4
Substitute in x = 4
16 - 3y = 7
- 3y = -9
y = 3