3 Variable simultaneous equations help.?

1 = a + b + c …… [1]
4 = 8a + 4b + 2c + 6 …… [2]
9 = 27a + 9b + 3c + 6 …… [3]

From [1] :
c = 1 - a - b …… [4]

Substitute [4] into [2] :
4 = 8a + 4b + 2(1 - a - b) + 6
4 = 8a + 4b + 2 - 2a - 2b + 6
6a + 2b = -4
3a + b = -2 …… [5]

Substitue [4] into [3] :
9 = 27a + 9b + 3(1 - a - b) + 6
9 = 27a + 9b + 3 - 3a - 3b + 6
24a + 6b = 0
4a + b = 0
b = -4a …… [6]

Substitute [6] into [5] :
3a + (-4a) = -2
-a = -2
a = 2

Substitue a = 2 into [6] :
b = -4(2)
b = -8

Substitute a = 2 and b = -8 into [4] :
c = 1 - (2) - (-8)
c = 7

Hence, a = 2, b = -8, c = 7

(1) : a + b + c = 1

(1) : c = 1 - a - b


(2) : 8a + 4b + 2c + 6 = 4

(2) : 8a + 4b + 2c = - 2 → you divide by 2 both sides

(2) : 4a + 2b + c = - 1 → recall (1) : c = 1 - a - b

(2) : 4a + 2b + 1 - a - b = - 1

(2) : 3a + b = - 2

(2) : b = - 2 - 3a



(3) : 27a + 9b + 3c + 6 = 9

(3) : 27a + 9b + 3c = 3 → you divide by 3 both sides

(3) : 9a + 3b + c = 1 → recall (1) : c = 1 - a - b

(3) : 9a + 3b + 1 - a - b = 1

(3) : 8a + 2b = 0 → you divide by 2 both sides

(3) : 4a + b = 0 → recall (2) : b = - 2 - 3a

(3) : 4a - 2 - 3a = 0

→ a = 2


Recall (2) : b = - 2 - 3a

b = - 2 - 6

→ b = - 8


Recall (1) : c = 1 - a - b

c = 1 - 2 + 8

→ c = 7