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Question 805699: use matrices and row operations to solve the following system;
2x+y+z=4
x+y-z=-3
5x-y+2z=23
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! use matrices and row operations to solve the following system;
2x+y+z=4
x+y-z=-3
5x-y+2z=23
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Rearrange::
x+y-z = -3
2x+y+z = 4
5x-y+2y = 23
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Subtract 2 times the 1st row from the 2nd row
Subtract 5 times the 1st row from the 3rd row
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x+y-z = -3
0-y+3z = 10
0-6y+7z = 38
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Subtract 6 times the 2nd row from the 3rd:
x+y-z = -3
0-y+3z = 10
0+0-11z = -22
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Solve the 3rd to get z = 2
Substitute into the 2nd to get: -y+3*2 = 10 ; y = -4
Substitute into the 1st to get: x -4 -2 = -3 ; x = 3
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Using the Matrix function of my TI-84 I checked my answer and got:
x = 3
y = -4
z = 2
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Cheers,
Stan H.
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