Simultaneous_Equations

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Slide 1:

Simultaneous Equations

Slide 2:

A few hints . . . (1) Scale up each term in one, or both equations to make the same number in front of either the x terms or the y terms. (2) Subtract if the signs in front of these are the same . (3) Add if the signs in front of these are different .

Slide 3:

5x + y = 20 2x + y = 11 … (1) … (2) Number the Equations 3x = 9 Subtract (to get rid of a letter) Divide (to find x) x = 3 Substitute in (2) (to find y) 2 x 3 + y = 11 6 + y = 11 y = 5 1

Slide 4:

7x + y = 43 3x + y = 23 … (1) … (2) Number the Equations 4x = 20 Subtract (to get rid of a letter) Divide (to find x) x = 5 Substitute in (2) (to find y) 3 x 5 + y = 23 15 + y = 23 y = 8 2

Slide 5:

8x + 3y = 57 6x + 3y = 51 … (1) … (2) Number the Equations 2x = 6 Subtract (to get rid of a letter) Divide (to find x) x = 3 Substitute in (2) (to find y) 6 x 3 + 3y = 51 18 + 3y = 51 y = 11 3 3y = 33

Slide 6:

3x + y = 19 x - y = 1 … (1) … (2) Number the Equations 4x = 20 Add (to get rid of a letter) Divide (to find x) x = 5 Substitute in (2) (to find y) 1 x 5 - y = 1 5 - y = 1 y = 4 4

Slide 7:

7x + 2y = 32 3x - 2y = 8 … (1) … (2) Number the Equations 10x = 40 Add (to get rid of a letter) Divide (to find x) x = 4 Substitute in (2) (to find y) 3 x 4 - 2y = 8 12 - 2y = 8 y = 2 5 2y = 4

Slide 8:

9x + 4y = 82 3x - 4y = -10 … (1) … (2) Number the Equations 12x = 72 Add (to get rid of a letter) Divide (to find x) x = 6 Substitute in (2) (to find y) 3 x 6 - 4y = -10 18 - 4y = -10 y = 7 6 4y = 28

Slide 9:

Simultaneous Equations - Scaling up -

Slide 10:

A few hints - Reminder . . . (1) Scale up each term in one, or both equations to make the same number in front of either the x terms or the y terms. (2) Subtract if the signs in front of these are the same . (3) Add if the signs in front of these are different .

Slide 11:

2x + 3y = 13 4x - y = 5 … (1) … (2) Number the Equations 14x = 28 Add (to get rid of a letter) Divide (to find x) x = 2 Substitute in (2) (to find y) 4 x 2 - y = 5 8 - y = 5 y = 3 7 2x + 3y = 13 12x - 3y = 15 … (1) … 3 x (2) Scale up one of the equations

Slide 12:

6x + 5y = 57 3x + y = 24 … (1) … (2) Number the Equations -9x = -63 Subtract (to get rid of a letter) Divide (to find x) x = 7 Substitute in (2) (to find y) 3 x 7 + y = 24 21 + y = 24 y = 3 8 6x + 5y = 57 15x + 5y = 120 … (1) … 5 x (2) Scale up one of the equations

Slide 13:

12x - 2y = 8 5x + y = 18 … (1) … (2) Number the Equations 22x = 44 Add (to get rid of a letter) Divide (to find x) x = 2 Substitute in (2) (to find y) 5 x 2 + y = 18 10 + y = 18 y = 8 9 12x - 2y = 8 10x + 2y = 36 … (1) … 2 x (2) Scale up one of the equations

Slide 14:

7x - 3y = 29 2x + 5y = 20 … (1) … (2) Number the Equations 41x = 205 Add (to get rid of a letter) Divide (to find x) x = 5 Substitute in (2) (to find y) 2 x 5 + 5y = 20 10 + 5y = 20 y = 2 10 5y = 10 35x - 15y = 145 6x + 15y = 60 … 5 x (1) … 3 x (2) Scale up both of the equations

Slide 15:

6x - 2y = 48 5x - 3y = 36 … (1) … (2) Number the Equations 8x = 72 Subtract (to get rid of a letter) Divide (to find x) x = 9 Substitute in (2) (to find y) 5 x 9 - 3y = 36 45 - 3y = 36 y = 3 11 3y = 9 18x - 6y = 144 10x - 6y = 72 … 3 x (1) … 2 x (2) Scale up both of the equations

Slide 16:

2x + 3y = 75 7x + 4y = 191 … (1) … (2) Number the Equations -13x = -273 Subtract (to get rid of a letter) Divide (to find x) x = 21 Substitute in (2) (to find y) 7 x 21 + 4y = 191 147 + 4y = 191 y = 11 12 4y = 44 8x + 12y = 300 21x + 12y = 573 … 4 x (1) … 3 x (2) Scale up both of the equations