Question 304165
I'm not sure how to do this problem at all in my algebra class with solving the system of equations.
3x      +14z = 80
       y-7z  =-30
 x-2y        =12
The solution is (__,__,__)
Please help with this problem

lets try to make this as easy as possible so you can do the same thing with other problems of this nature:
line all the coefficients on the variables up and the 3 solutions as well like so:
And we are going to use elimination...
Elimination means in this case to use a process of multiplication and addition to try to isolate variables and solve for them easier...
 3x + 0y + 14z =  80
 0x +  y -  7z = -30 (multiply by 2)
  x - 2y +  0z =  12
to get
 3x + 0y + 14z =  80
 0x + 2y - 14z = -60 (add to top row)
  x - 2y +  0z =  12
to get
 3x + 2y +  0z =  20
 0x + 2y - 14z = -60
  x - 2y +  0z =  12 (add to top row)
to get
 4x + 0y +  0z =  32
 0x + 2y - 14z = -60
  x - 2y +  0z =  12
now you got
 4x = 32 so x = 8 (one variable solved and one row cleared)
plug in
 0x + 2y - 14z = -60 -->  2y - 14z = -60
  8 - 2y +  0z =  12 --> -2y +  0z =   4
now you got
 -2y = 4 so y = -2 (another variable solved and another row cleared)
plug in
 -4 - 14z = -60 --> -14z = -56
so z = 4 (last variable solved)
check:
 3(8) + 0(-2) + 14(4) =  80 --> 24 + 56 =  80 yes
 0(8) +  (-2) -  7(4) = -30 --> -2 - 28 = -30 yes
  (8) - 2(-2) +  0(4) =  12 -->  8 +  4 =  12 yes