Question

1 =A+2B
-8 =2C+B
0 =4A+C

Solve for A, B & C

Answer 1

Take the third equation and subtract 4A from both sides

-4A = C

Take -4A and substitute into the second equation so -8 = 2C + B turns into

-8 = 2(-4A) + B

take the first equation and the new equation in the previous line and

Answer 2

... subtract the first equation from TWICE new equation

-16 = -16A + 2B
1 = A + 2B

to get

-17 = -17A

so A = 1 which means from -4A = C that

-4(1) = C = -4

and from the first equation

1 = 1 + 2B or B = 0

Answer 3

Using elimination, which is very methodical, is a good way to go

1 =A+2B
-8 =2C+B
0 =4A+C

use elimination. First, put the coefficients in order
A B C
1 2 0 1
0 1 2 -8
4 0 1 0

multiply the first row by -4 and add to the third row

1 2 0 1
0 2 2 -8
0 -8 1 -4

multiply 2nd row by 4 and add to third row
1 2 0 1
0 2 2 -8
0 0 9 -36

backsolve (work from bottom up)
C= -36/9 = -4
2B -8 = -8, B=0
A +2*0 +0* -4= 1, A=1