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Discriminant

The equations...

Question

The equations $x + 4 y - 2 z = 3$ , $3 x + y + 5 z = 7$ and $2 x + 3 y + z = 5$ have

a unique solution

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no solution

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two solutions

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infinite solutions

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Solution

The correct option is B no solution
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 4 & - 2 3 & 1 & 5 2 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣ = 1 (1 - 15) - 4 (3 - 10) - 2 (9 - 2) = 0$
and $Δ_{1}$ is not zero
Therefore, it has no solution

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Similar questions

x + 4 y - 2 z = 3

3 x + y + 5 z = 7

2 x + 3 y + z = 5

x + 4 y - 2 z = 3

3 x + y + 5 z = 7

2 x + 3 y + z = 5

x + 4 y - 2 z = 3, 3 x + y + 5 z = 7

2 x + 3 y + z = 5

2 x + 3 y + z = 5, 3 x + y + 5 z = 7, x + 4 y - 2 z = 3

3 x - 4 y + 2 z = - 1

2 x + 3 y + 5 z = 7

x + z = 2

x = ?

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