Question

PLEASE HELP!!!
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

Answer 1

I, myself, would use the elimination method, because there is 3 unknown variables.
2x + y + z = - 7
x - 3y + 4z = - 14 -->(-2)x - 3y + 4z = - 14
---------------
2x + y + z = - 7
-2x + 6y - 8z = 28 (result of multiplying by -2)
---------------add
0 + 7y - 7z = 21
7y - 7z = 21

x - 3y + 4z = - 14--->(-1)x - 3y + 4z = - 14
x - 2y - 3z = - 11
----------------
-x + 3y - 4z = 14 (result of multiplying by -1)
x - 2y - 3z = - 11
----------------add
0 + y - 7z = 3
y - 7z = 3

7y - 7z = 21
y - 7z = 3 -->(-1)y - 7z = 3
------------
7y - 7z = 21
-y + 7z = - 3 (result of multiplying by -1)
------------add
6y + 0 = 18
6y = 18
y = 3
now sub 3 in for y
y - 7z = 3
3 - 7z = 3
3 - 3 = 7z
0 = 7z
z = 0
now sub known answers into one of the original equations
2x + y + z = - 7
2x + 3 + 0 = - 7
2x + 3 = - 7
2x = -7 -3
2x = - 10
x = - 5
check...
x - 3y + 4z = - 14
-5 - 3(3) + 4(0) = - 14
-5 - 9 + 0 = - 14
-14 = - 14 (correct)
ANSWER : x = -5, y = 3, and z = 0 or (-5,3,0)

Answer 2

@danny562 .....I did what I could :)

Answer 3

@kelliegirl33 a great response. I wrestled with this last night, and got in trouble with a sign for the x value (x=5) which kept me from solving it. Reviewing your work was a great help and the methodical way you solved.