SOLUTION: x1+x2+x3=6 2x1-x2+3x3=4 4x1+5x2-10x3=13

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Question 1099131: x1+x2+x3=6
2x1-x2+3x3=4
4x1+5x2-10x3=13
Found 2 solutions by Fombitz, Boreal:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use Cramer's rule,
A=%28matrix%283%2C3%2C%0D%0A1%2C1%2C1%2C%0D%0A2%2C-1%2C3%2C%0D%0A4%2C5%2C-10%29%29
abs%28A%29=41
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A%5Bx1%5D=%28matrix%283%2C3%2C%0D%0A6%2C1%2C1%2C%0D%0A4%2C-1%2C3%2C%0D%0A13%2C5%2C-10%29%29
abs%28A%5Bx1%5D%29=82
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A%5Bx2%5D=%28matrix%283%2C3%2C%0D%0A1%2C6%2C1%2C%0D%0A2%2C4%2C3%2C%0D%0A4%2C13%2C-10%29%29
abs%28A%5Bx2%5D%29=123
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A%5Bx3%5D=%28matrix%283%2C3%2C%0D%0A1%2C1%2C6%2C%0D%0A2%2C-1%2C4%2C%0D%0A4%2C5%2C13%29%29
abs%28A%5Bx3%5D%29=41
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x%5B1%5D=abs%28A%5Bx1%5D%29%2Fabs%28A%29=82%2F41=2
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x%5B2%5D=abs%28A%5Bx2%5D%29%2Fabs%28A%29=123%2F41=3
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x%5B3%5D=abs%28A%5Bx3%5D%29%2Fabs%28A%29=41%2F41=1

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x1+x2+x3=6
2x1-x2+3x3=4
4x1+5x2-10x3=13
===================Add the first two
3x1+4x3=10; add 5 times the second to the third
14x1+5x3=33
-5 times the first + 4 times the second
-15x1-20x3=-50
56x1+20x3=132
41x1=82
x1=2
2+x2+x3=6
4-x2+3x3=4
4x3=4
x3=1
x2=3
(2, 3, 1)
check in the second and works
check in third and works.