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lys-0071 [83]
2 years ago
6

2x1+0x2+3x3=3

Mathematics
1 answer:
Alexxx [7]2 years ago
6 0

[1] … … 2<em>x</em>₁ + 0<em>x</em>₂ + 3<em>x</em>₃ = 3

[2] … … 4<em>x</em>₁ - 3<em>x</em>₂ + 7<em>x</em>₃ = 5

[3] … … 8<em>x</em>₁ - 9<em>x</em>₂ + 15<em>x</em>₃ = 10

Since [1] is already free of <em>x</em>₂, you might as well start by eliminating <em>x</em>₂ from the other two equations. Add -3 times [2] to [3] :

-3 (4<em>x</em>₁ - 3<em>x</em>₂ + 7<em>x</em>₃) + (8<em>x</em>₁ - 9<em>x</em>₂ + 15<em>x</em>₃) = -3 (5) + 10

-12<em>x</em>₁ + 9<em>x</em>₂ - 21<em>x</em>₃ + 8<em>x</em>₁ - 9<em>x</em>₂ + 15<em>x</em>₃ = -15 + 10

-4<em>x</em>₁ - 6<em>x</em>₃ = -5

[4] … … 4<em>x</em>₁ + 6<em>x</em>₃ = 5

Now eliminate <em>x</em>₃ in [1] and [4]. Add -2 times [1] to [4] :

-2 (2<em>x</em>₁ + 3<em>x</em>₃) + (4<em>x</em>₁ + 6<em>x</em>₃) = -2 (3) + 5

-4<em>x</em>₁ - 6<em>x</em>₃ + 4<em>x</em>₁ + 6<em>x</em>₃ = -6 + 5

0 = -1

which is a contradiction. This means the system has no solution.

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