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Question 632151: Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.
2x + y + z = –7
x – 3y + 4z = –14
x – 2y – 3z = –11
Found 2 solutions by ankor@dixie-net.com, solver91311:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 2x + y + z = –7
x – 3y + 4z = –14
x – 2y – 3z = –11
We can use elimination here, Multiply the 1st equation by -1
-2x -y - z = 7
x – 3y + 4z = –14
x – 2y – 3z = –11
---------------------Adding eliminates x and z, find y
0 - 6y = - 18
y = -18/-6
y = +3
:
Find x and z
Use the 2nd and 3rd equations, replace y with 3
x – 3(3) + 4z = –14
x – 2(3) – 3z = –11
:
x - 9 + 4z = -14
x - 6 - 3z = -11
:
x + 4z = -14 + 9
x - 3z = -11 + 6
:
x + 4z = -5
x - 3z = -5
--------------subtraction eliminates x find z
7z = 0
z = 0
therefore
x = -5
:
Check solutions in the 1st original equation
2x + y + z = –7
2(-5) + 3 + 0 =
-10 + 3 = -7
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Gauss-Jordan was pretty clean on this one, while substitution was a little ugly. Regular elimination was reasonably tidy also. But my favorite, just because I can use the MDETERM function to get the determinant of a matrix that I have entered into Excel (this function is also available in the Numbers program on the Mac), is to use Cramer's rule.
John
My calculator said it, I believe it, that settles it
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