SOLUTION: 3x+2y-2z=14 2x-5y+3z=7 4x-3y+7z=5

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Question 770111: 3x+2y-2z=14
2x-5y+3z=7
4x-3y+7z=5
Found 2 solutions by Cromlix, Alan3354:
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
3x+2y-2z=14....(1)
2x-5y+3z=7.....(2)
4x-3y+7z=5.....(3)
Multiply (1) by 2
Multiply (2) by 3
6x + 4y - 4z = 28....(1)
6x - 15y +9z = 21.....(2)
Subtract:
19y - 13z = 7 Equation A
Multiply (2) by 2
4x - 10y + 6z = 14....(2)
Subtract (3)
4x - 10y + 6z = 14....(2)
4x - 3y + 7z = 5......(3)
Subtract
-7y - z = 9 Equation B
......................
Consider Equations A and B
19y - 13z = 7.....(A)
-7y - z = 9.....(B)
Multiply (B) by 13 and
subtract from (A)
19y - 13z = 7.....(A)
-91y - 13z = 117...(B)
110y = -110
y = -1.
Substitute y = -1 into
Equation A
19y - 13z = 7.....(A)
19(-1) - 13z = 7
-19 - 13z = 7
-13z = 7 + 19
-13z = 26
z = -2
..................
Substituting y = -1 and z = -2
into Equation 1
3x+2y-2z=14....(1)
3x + 2(-1)-2(-2) = 14
3x -2 + 4 = 14
3x = 14 - 2
3x = 12
x = 4.
x = 4, y = -1, z = -2
Hope this helps.
:-)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3x+2y-2z=14
2x-5y+3z=7
4x-3y+7z=5
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Multiply eqn 2 by -2, then add to eqn 3.
Leaves an eqn in y & z
---
Multiply eqn 2 by -3, multiply eqn 1 by 2, then add.
Leaves another eqn in y & z
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Solve for y & z, then solve for x
==============
(4,-1,-2) is the answer.