Question

Solve the simultaneous questions:

(a) x+y+z=-3 (1)
x-y-2z=13 (2)
y-4z=25 (3)

(b)x+2y+3z=-14 (1)
2x+3y-z=13 (2)
3x-y+2z=-7 (3)

Answer 1

http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

for the first one for example there are three rows and four columns

1 +1 +1 -3
1 -1 -2 13
1 +0 -4 25

Answer 2

x = 15/7
y = 4/7
z = -40/7

Answer 3

There is no unique or best way to solve these.
After doing a few you get a "feel" of what to look for.
e.g. for your first one, notice that last one says:
y - 4z = 25 , so y = 25+4z
- could be useful

look at the first two, they both have 1x
so lets subtract the 2nd from the 1st:
2y + 3z = - 16
remember y = 25+4z
2(25+4z) + 3z = -16
50 + 8z + 3z = -16
11z = -66
z = -6
then y = 25 + 4(-6) = 1

back in the 1st:
x+y+z=-3
x+1-6=-3
x = 2

x=2 , y=1 , z=-6

hint for the 2nd:
double the first and subtract from the 2nd to get a
y , z equation
triple the first and subtract from the 3rd to get another y , z equation
now solve as 2 equations in two unknowns