1. Simultaneous Equations –
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Simultaneous Equations –
Bar Modelling

2. Simultaneous Equations
28 November 2018
Simultaneous Equations

3. = 34 = 31 = 3 = 31 = 25 = 5 5x + 3y = 34 Bar Modelling 5x + 2y = 31 x

5. 3x + 4y = 20 4x + 2y = 30 2x + 3y = 26 3x + 3y = 18 5x + 2y = 36
Choose 1, 2 or 3 Simultaneous Equations.
Use your whiteboard to draw the equations with bar models.
How can you use the bar models to eliminate a variable?
3x + 4y = 20
4x + 2y = 30
2x + 3y = 26
3x + 3y = 18
5x + 2y = 36
4x + 4y = 44
y = 2
x = 4
y = 3
x = 6
y = 4
x = 7
3x + 2y = 16
4x + 2y = 18
6x + 3y = 30
5x + 4y = 30
y = 2
x = 4
y = 5
x = 2
4x + 2y = 17
How can you model a
negative coefficient?
4x + 3y = 36
5x + 3y = 22.5
5x - 3y = 18
y = 2.5
x = 3
y = 4
x = 6

6. Subtract the bottom bar model from the top
Question 1 (Red)
Question 2 (Red)
3x + 4y = 20
4x + 2y = 30
3x + 3y = 18
5x + 2y = 36 x x x y y y y
= 20 x x x y y y
= 18
Subtract the bottom bar model from the top
and draw it here.
What is the value of y?

8. + 2x + 3y = 22 x - 3y = 2 x + 6y = 20 3x = 24 = 22 = 2 = 24 y = 2
What’s the challenge?
x - 3y = 2
x = 8
We can see we should eliminate the y variable.
If we subtract the second equation…
x + 6y = 20
= 22 x x y x
= 2 y +
= 24 x x
3x = 24

10. + 4x + 2y = 50 3x - 2y = 20 = 50 = 20 = 70 y = 5 x = 10 x x x x y y x

11. + 6x + 4y = 46 3x - 4y = -19 = 46 = -19 = 27 y = 7 x = 3 x x x x x x y

13. y = 4x + y = 19 y = 6x + 2y = 47 3x - y = 9 x = 5x - 2y = 30 x = y =
Use bar models to help you solve these simultaneous equations.
Substitute your values back in the equations to check your answer.
y =
4x + y = 19
y =
6x + 2y = 47
3x - y = 9
x =
5x - 2y = 30
x =
y =
x + 3y = -6
y =
4x + 2y = 18
5x - 3y = 42
x =
3x - 4y = -14
x =

14. y = 2.5 4x + y = 19 y = 3 6x + 2y = 47 3x - y = 9 x = 4 5x - 2y = 30
Use bar models to help you solve these simultaneous equations.
Substitute your values back in the equations to check your answer.
y = 2.5
4x + y = 19
y = 3
6x + 2y = 47
3x - y = 9
x = 4
5x - 2y = 30
x = 7
y = 5
x + 3y = -6
y = -4
4x + 2y = 18
5x - 3y = 42
x = 6
3x - 4y = -14
x = 2

15. I can solve simultaneous equations by eliminating a variable.
Comment in your book.
I can solve simultaneous equations by eliminating a variable.
I can solve simultaneous questions involving negative coefficients.
I can solve simultaneous questions by rearranging equations.