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Question 931406: -0.4x + 0.3y +0 z =0
0.2x -0.6 y +0.3 z =0
1x + 1y + 1z =1
solve using row elimination method not by determinant
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! -0.4x + 0.3y + 0z = 0
0.2x - 0.6y + 0.3z = 0
1x + 1y + 1z = 1
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put the system of linear equations into standard form
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-0.4x + 0.3y + 0z = 0
0.2x - 0.6y + 0.3z = 0
1x + 1y + 1z = 1
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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 = 0.23076923
y = 0.30769231
z = 0.46153846
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now by elimination:
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-0.4x + 0.3y + 0z = 0
0.2x - 0.6y + 0.3z = 0
1x + 1y + 1z = 1
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-0.4x + 0.3y + 0z = 0
2(0.2x - 0.6y + 0.3z = 0)
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-0.4x + 0.3y + 0z = 0
0.4x - 1.2y + 0.6z = 0
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add the two equations:
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-0.9y + 0.6z = 0
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0.2x - 0.6y + 0.3z = 0
-0.2(1x + 1y + 1z = 1)
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0.2x - 0.6y + 0.3z = 0
-0.2x - 0.2y - 0.2z = -0.2
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add the two equations:
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-0.8y + 0.1z = -0.2
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-0.9y + 0.6z = 0
-6(-0.8y + 0.1z = -0.2)
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-0.9y + 0.6z = 0
4.8y - 0.6z = 1.2
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add the two equations:
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3.9y = 1.2
y = 1.2/3.9
y = 0.307692307692
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-0.9y + 0.6z = 0
-0.9*0.307692307692 + 0.6z = 0
z = 0.9*0.307692307692 / 0.6
z = 0.461538461538
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-0.4x + 0.3y + 0z = 0
-0.4x + 0.3*0.307692307692 = 0
-0.4x = -0.3*0.307692307692
x = -0.3*0.307692307692/-0.4
x = 0.230769230769
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solution by elimination:
x = 0.23076923
y = 0.30769231
z = 0.46153846
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