Simultaneous Equations –

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Presentation transcript:

Simultaneous Equations – goteachmaths.co.uk Simultaneous Equations – Bar Modelling

Simultaneous Equations 28 November 2018 Simultaneous Equations

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

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

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?

+ 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

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

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

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 =

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

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.