SOLUTION: solve algebraically: 6x-3y+8z=4 -x+9y--2z=2 4x+6y-4z=3 A) (5/2, 5/3, -3/4) B) (1,-2,-1) C) (1/2, 1/3, 1/4) d) (5, -2, 5/4)

Question 208502: solve algebraically: 6x-3y+8z=4
-x+9y--2z=2
4x+6y-4z=3

A) (5/2, 5/3, -3/4)
B) (1,-2,-1)
C) (1/2, 1/3, 1/4)
d) (5, -2, 5/4)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
solve algebraically:
6x-3y+8z=4
-x+9y--2z=2 ?? I'll assume the -- is a typo.
4x+6y-4z=3
-----------
6x-3y+8z=4
-x+9y-2z=2
4x+6y-4z=3
----------
I'll use elimination & substitution
Since z has 2, 4 and 8 for coefficients, eliminate it
-x+9y-2z=2 x2 --> -2x+18y-4z = 4
+4x+6y-4z=3
-2x+18y-4z=4
---------- Subtract
6x-12y = -1 Eqn A
-----------
6x-3y+8z=4
-x+9y-2z=2 x4 --> -4x+36y-8z=8
-----------
+6x-3y+8z=4
-4x+36y-8z=8
------------ Add
2x+33y = 12 Eqn B
6x-12y = -1 Eqn A
6x+99y = 36 Eqn b x 3
----------- Subtract
-111y = -37
y = 1/3
Now sub for y into Eqn A or B to find x
2x+33y = 12 Eqn B
2x+11 = 12
x = 1/2
-------
Sub x & y into one of the originals to find z
4x+6y-4z=3
2 + 2 -4z = 3
-4z = -1
z = 1/4

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