Solving systems of linear equations in three variables.

Question

Ok so i don't really totally get these problems. Can you help me solve this one? and explain everything please?

2x+3y=6+z
x-2y=-1-z
3x+y=-1+3z

Answer 1

put them in standard form (x,y,z)

2x+3y-z=6
x-2y+z=-1
3x+y-3z=-1

You can solve these a number of ways, I will show you one.
add 1st and second equations
3x+y=5
now multiply equation 2 by three, then add equations 2 and 3.
6x-5y=-4 check that.
now on these two remaining equations, multiply the first by 2, then subtract.
7y=14
y=2 work back up to find x, then z.

Answer 2

Ok, this helps a lot, but hold on, i don't get how you got 7y=14? because when i multiply 3x+y=5 by (-2) i get -6x-2y=8. And then when combining that with 6x-5y=-4 i get -7y=4? how did you get 7y=14???

Answer 3

3x+y=5 multiply -2, your way
6x-5y=-4 to get

-6x-2y=-10
6x-5y=-4 add to get

-7y=-14
y=2

Answer 4

Oh wait, i forgot to multiply the 5 by -2! (idk how i got 8, but watever its not that important) so right you would get y=2.
ok i think i get it now! THANKS!