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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
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! 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
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