Simultaneous Equations by Substitution

10 Apr 2023

Solving Using the

Substitution Method

Solving Using the

Substitution Method

© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09 www.brain-cells.co.uk

y

x 1 2 3 4 5 6 7 8

1

2

3

4

5

6

7

8

–7 –6 –5 –4 –3 –2 –1 -1-2-3-4

x 1 2 3 4

y 4 5 6 7

x 1 2 3 4

y 2 4 6 8

Solve with a graphy = x + 3y = 2x

x = 3y = 6x = 3y = 6

© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09 www.brain-cells.co.uk

Solve, by substitution:

y = x + 3 (1)y = 2x (2)

Substitute the y in equation (1) with the 2x from equation (2) to obtain equation (3)

2x = x + 3 (3)

2x – x = 3 x = 3

Now put the value x = 3 into either of the two original equations to find the value of y

y = x + 3 (1)

y = 3 + 3

y = 6

x = 3y = 6x = 3y = 6

© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09 www.brain-cells.co.uk

1. y = x + 4 4. y = 2x + 1 y = 2x y = 3x

2. y = 2x + 7 5. y = x + 5 y = 3x y = 2x – 3

3. y = x – 5 6. y = x – 7 y = 2x y = 3x – 11

© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09 www.brain-cells.co.uk

1. y = x + 4 4. y = 2x + 1 y = 2x y = 3x

x = 4 and y = 8 x = 1 and y = 32. y = 2x + 7 5. y = x + 5 y = 3x y = 2x – 3x = 7 and y = 21 x = 8 and y = 133. y = x – 5 6. y = x – 7 y = 2x y = 3x – 11x = -5 and y = -10 x = 2 and y = -5

© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09 www.brain-cells.co.uk

1. y = x2 + 2x – 8

y = 6 – 3x

6 – 3x = x2 + 2x – 8

0 = x2 + 2x + 3x – 8 – 6

0 = x2 + 5x – 14

0 = (x + 7)(x – 2)

x = -7 and +2

1 x –14 = -14

2 x – 7 = -14

7 x – 2 = -14

14 x –1 = -14

Choose the pair with a sum of 5

7 + -2 = 5

7 – 2 = 5© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09 www.brain-cells.co.uk

1. y = x2 + 8x + 12 4. y = x2 – 4x – 7

y = x y = 3 – x

2. y = x2 + 8x + 10 5. y = x2 – 5x – 35

y = 3x y = 2x – 5

3. y = x2 – 5x – 5 6. y = x2 + x

y = 1 – 4x y = x2 + 25

© Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09 www.brain-cells.co.uk

1. y = x2 + 8x + 12 4. y = x2 – 4x – 7

y = x y = 3 – x

x = -3 and -4 x = -2 and 5

2. y = x2 + 8x + 10 5. y = x2 – 5x – 35

y = 3x y = 2x – 5

x = -2 and -5 x = -3 and 10

3. y = x2 – 5x – 5 6. y = x2 + x

y = 1 – 4x y = x + 25

x = -2 and 3 x = -5 and 5 © Brain-Cells: E.Resources Ltd. All Rights Reserved 24/11/09 www.brain-cells.co.uk