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

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 6 + y = 15 x × 2 Step 4 – Using the value of x in equation 1 or 2 find the value of y. 12 + y = 15 y = 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

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 8 - y = 5 y = 3

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

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)

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. 8 + 6y = 54 x × 3 24 + 6y = 54 y = 5 6y = 30

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 TASK 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)                         8

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

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 Menu Answers

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 Menu Answers

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