What is a+2b+3c=0,a+b=0,b+3c=0 ?

The solution to a+2b+3c=0,a+b=0,b+3c=0 is a=3c,b=-3c

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a+2b+3c=0,a+b=0,b+3c=0

a + 2 b + 3 c = 0, a + b = 0, b + 3 c = 0

a = 3 c, b = - 3 c

Solution steps

a + 2 b + 3 c = 0 a + b = 0 b + 3 c = 0

Isolate

a

for

a + b = 0 : a = - b

Substitute

a = - b

[b + 3 c = 0 - b + 2 b + 3 c = 0]

Simplify

[b + 3 c = 0 b + 3 c = 0]

Isolate

b

for

b + 3 c = 0 : b = - 3 c

Substitute

b = - 3 c

[- 3 c + 3 c = 0]

Simplify

[0 = 0]

For

a = - b

Expressing

a

in terms of

c

a = - (- 3 c)

Simplify

a = 3 c

The solutions to the system of equations are:

a = 3 c, b = - 3 c

3 x + 2 y = 6, 3 x - y = 0

x + y = 0, 2 x - y = 9

2 x - y + 2 z = - 4, 6 x - 3 y + 6 z = - 12, - 4 x + 2 y - 4 z = 8

f (x) = 2, (x + 3) = 3 (2 x^{7})

1.34 x - 6 y = 0, x + 2 y = 14

What is a+2b+3c=0,a+b=0,b+3c=0 ?
The solution to a+2b+3c=0,a+b=0,b+3c=0 is a=3c,b=-3c