1. Simultaneous Equations –
goteachmaths.co.uk
Simultaneous Equations –
Elimination

2. Simultaneous Equations
05 December 2018
Simultaneous Equations

4. How can we check we’re correct?
How do we find x?
How do we find y?
9y - 12 = 15
6x + 35 = 95
(-35)
(- 35)
(+12)
(+12)
6x = 60
9y = 27
(÷6)
(÷6)
(÷9)
(÷9)
x = 10
y = 3
How can we check we’re correct?

5. Simultaneous Equations
05 December 2018
= £3.50
= £2.50
How much is a packet of quavers?

6. We can find the difference
between two sums.

7. = £3.50 -
= £2.50 £1 £1
= £1
How much is a Dairy Milk?

8. = £7 -
= £5 £2 £2
50p
50p
= £2
Cost of 1 Pringles?
Cost of 1 apple?

9. - = £8 = £6 X X X X Y Y 8 4x + 2y = 8 4x + 1y = 6 0 + 1y = 2 y = 2
Put y back in.
4x + 2 = 6
4x = 4
x = 1

10. = £11 = £7 3x + 4y = 11 3x + 2y = 7 Put y back in. 0 + 2y = 4
3x + (2x2) = 7
y = 2
3x + 4 = 7
3x = 3
x = 1

11. Simultaneous Equations
Elimination Method
5x + 3y = 65
6x + 4y = 36
6x + 2y = 20
5x + 2y = 60
6x + 2y = 30
4x + 2y = 16
0x + y = 5
2y = 6
2x + 0y = 4
y = 3
y = 5
2x = 4
x = 2
Put y back in.
Put y back in.
Put x back in.
5x + (2x5) = 60
6x + (2x3) = 30
(4x2) + 2y = 16
6x + 6 = 30
5x + 10 = 60
8 + 2y = 16
6x = 24
5x = 50
2y = 8
x = 4
x = 10
y = 4

12. We can’t simply subtract. We need to change one equation first
6x + 6y = 30
We can’t simply subtract.
3x + 2y = 13
We need to change one equation first
3x + 2y = 13
(x2)
(x2)
6x + 6y = 30
6x + 4y = 26
6x + 4y = 26

14. Copy the question and process into your book!
3x + 4y = 17
3x + 4y = 39
3x + 4y = 18 1) 7)
13)
3x - 3y = 3
3x + 3y = 32
6x + 3y = 21
4x + 5y = 46
5x + 8y = 44
4x + 5y = 40
14) 2) 8)
4x - 2y = 4
5x + 6y = 38
8x + 2y = 48
3x + 2y = 23
7x + 11y = 80
3x + 2y = 17
15) 3) 9)
6x - 1y = 26
7x + 9y = 68
9x + 1y = 16
2x - 2y = 0
5x + 2y = 16
2x + 2y = 10
16) 4)
10)
8x - 4y = 8
2x + 2y = 10
10x + 3y = 43
4x - 2y = 30
9x + 3y = 51
4x + 2y = 12
17) 5)
11)
5x - 6y = 13
6x + 3y = 36
6x + 4y = 20
8x - 2y = 16
11x + 6y = 57
2x + 3y = 38
18) 6)
12)
7x - 7y = -7
9x + 6y = 51
5x + 9y = 107

15. Copy the question and process into your book!
x = 3
3x + 4y = 39
x = 5
3x + 4y = 18
x = 2
3x + 4y = 17 1) 7)
13)
y = 2
3x + 3y = 32
y = 6
3x - 3y = 3
6x + 3y = 21
y = 3
4x + 5y = 46
x = 4
5x + 8y = 44
x = 4
4x + 5y = 40
x = 5
14) 2) 8)
4x - 2y = 4
y = 6
5x + 6y = 38
y = 3
8x + 2y = 48
y = 4
x = 5
7x + 11y = 80
x = 2
3x + 2y = 17
x = 1
3x + 2y = 23
15) 3) 9)
7x + 9y = 68
y = 6
9x + 1y = 16
y = 7
6x - 1y = 26
y = 4
2x - 2y = 0
x = 2
5x + 2y = 16
x = 2
2x + 2y = 10
x = 4
16) 4)
10)
8x - 4y = 8
y = 2
2x + 2y = 10
y = 3
10x + 3y = 43
y = 1
4x - 2y = 30
x = 11
9x + 3y = 51
x = 5
4x + 2y = 12
x = 2
17) 5)
11)
5x - 6y = 13
y = 7
6x + 3y = 36
y = 2
6x + 4y = 20
y = 2
8x - 2y = 16
x = 3
11x + 6y = 57
x = 3
2x + 3y = 38
x = 7
18) 6)
12)
7x - 7y = -7
y = 4
9x + 6y = 51
y = 4
5x + 9y = 107
y = 8

16. Extension @ TESCO, Jimmy bought 14 cakes and
12 hotdogs for the party and paid £27.60.
@ TESCO, Sally paid £10.80 for 3 hotdogs
and 8 cakes for the party.
Use this information to make a pair of equations.
How much is 1 hotdog at TESCO?
Hotdog = 90p
Cake = £1.20

17. 5x + 4y = 33
x = 5
5x + 2y = 29
y = 2
3x + 5y = 27
x = 4
6x + 2y = 30
y = 3
2x + 2y = 12
x = 1
8x - 3y = -7
y = 5

18. I can solve simultaneous questions with positive coefficients.
Comment in your book.
I need more practice.
I can solve simultaneous questions with positive coefficients.
I can solve simultaneous questions with negative coefficients.