SOLUTION: x-9y+4z=1 -2x+9y-4z=-3 2x+y-4z=-3 What does x, y, and z equal! I need to solve either by substitution or elimination

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Question 924942: x-9y+4z=1
-2x+9y-4z=-3
2x+y-4z=-3
What does x, y, and z equal! I need to solve either by substitution or elimination
Found 2 solutions by TimothyLamb, stanbon:
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
x - 9y + 4z = 1
-2x + 9y - 4z = -3
2x + y - 4z = -3
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put the system of linear equations into standard form
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x - 9y + 4z = 1
-2x + 9y - 4z = -3
2x + y - 4z = -3
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = 2
y = 1
z = 2
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by elimination:
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x - 9y + 4z = 1
-2x + 9y - 4z = -3
2x + y - 4z = -3
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add equations 1 and 2:
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x - 9y + 4z = 1
-2x + 9y - 4z = -3
---
x + 4z = 1
-2x - 4z = -3
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-x = -2
x = 2
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add equations 2 and 3:
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-2x + 9y - 4z = -3
2x + y - 4z = -3
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9y - 4z = -3
y - 4z = -3
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10y - 8z = -6 (Equation A)
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substitute x=2 into equation 1:
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2 - 9y + 4z = 1
-9y + 4z = -1 (Equation B)
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add equations A and 2*B
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10y - 8z = -6
2(-9y + 4z = -1)
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10y - 8z = -6
-18y + 8z = -2
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-8y = -8
y = 1
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substitute x=2 y=1 into equation 1:
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2 - 9 + 4z = 1
4z = 8
z = 2
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answer:
x = 2
y = 1
z = 2
---
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Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x-9y+4z=1
-2x+9y-4z=-3
2x+y-4z=-3
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Add 2 times the 1st row to the 2nd row
Subtract 2 times the 1st row from the 3rd row
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x-9y+4z=1
0-9y+4z=-1
0+19y-12z=-5
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Add 3 times the 2nd row to the 3rd to get:
x-9y+4z=1
0-9y+4z=-1
0-8y=0=-8
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Solve the 3rd equation for "y"::
Add 3 times the 2nd row to the 3rd to get:
x-9y+4z=1
0-9y+4z=-1
y = 1
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Substitute y = 1 into the 2nd equation to solve for "z".
x-9y+4z=1
z = 2
y = 1
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Solve for "x":
x = 2
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Cheers,
Stan H.
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