a+b=1,2b+c=1,a+2c=1

Question

system of equation solve it

Answer 1

a + b + 0c = 1

0a + 2b + c = 1

a + 0b + 2c = 1

In the first equation, subtract out the third equation:

(also, don't write the third equation again, since we've used it)

0a + b - 2c = 0

0a + 2b + c = 1

Multiply the second equation by 2 on both sides:

0a + b - 2c = 0

0a + 4b + 2c = 2

Add the first and second equation together:

0a + 5b + 0c = 2

b = 2/5

But since we know that b - 2c = 0 (see 5 lines above), we can do this:

2/5 - 2c = 0

-2c = -2/5

c = 1/5

Since we know a + b = 1 (original problem), we can do this:

a + 2/5 = 1

a = 3/5

Answer:  a = 3/5, b = 2/5, c = 1/5