SOLUTION: Dear Tutor, I am getting so many different answers with this...Please help! Direction is solve the system of equations Solve for x only 4x + 2y + z = 24 2x - 3y

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Question 193815This question is from textbook Basic Technical Mathematics
: Dear Tutor,
I am getting so many different answers with this...Please help!
Direction is solve the system of equations
Solve for x only
4x + 2y + z = 24
2x - 3y - z = 2
5x + y + 2z = 21 This question is from textbook Basic Technical Mathematics

Found 3 solutions by scott8148, Alan3354, stanbon:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website!
adding 1st and 2nd equations gives ___ 6x-y=26 (A)

multiplying 2nd equation by 2 and adding 3rd equation gives ___ 9x-5y=25 (B)

multiplying equation (A) by -5 ___ -30x+5y=-130
adding equation (B) ___ -21x=-105
dividing by -21 ___ x=5

Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
Solve for x only
4x + 2y + z = 24
2x - 3y - z = 2
5x + y + 2z = 21
-----------------
Eliminate z
Add the 1st and 2nd eqn
4x + 2y + z = 24
2x - 3y - z = 2
----------------
6x - 1y = 26 eqn A
Multiply the 2nd eqn by 2, then add the 3rd.
4x - 6y -2z = 4
5x + y + 2z = 21
----------------
9x - 5y = 25 eqn B
---------------
Now you have 2 eqns in 2 unknowns, not 3.
Multiply eqn A by 5 and subtract eqn B.
30x - 5y = 130 eqn A times 5
9x - 5y = 25 eqn B
-------------
21x = 105
x = 5

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
Solve for x only
-----------------------
4x + 2y + z = 24
2x - 3y - z = 2
5x + y + 2z = 21
------------------------
Add the 1st Eq. to the 2nd ; Subtract 2 times the 1st from the 3rd to get:
4x + 2y + z = 24
6x - y + 0 = 26
-3x - 3y - 0 = -27
------------------------
Subtract 3 times the 2nd Eq. from the 3rd to get:
4x + 2y + z = 24
6x - y + 0 = 26
-21x + 0 - 0 = -105
---------------------------
Solve the 3rd equation:
x = 5
=============================
Cheers,
Stan H.

SOLUTION: Dear Tutor, I am getting so many different answers with this...Please help! Direction is solve the system of equations Solve for x only 4x + 2y + z = 24 2x - 3y - z = 2 5x