The system of equations $x + 2 y + 3 z = 4, 2 x + 3 y + 4 z = 5, 3 x + 4 y + 5 z = 6$ has

Infinitely many solutions

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No solution

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Unique solution

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None of these

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Solution

The correct option is A Infinitely many solutions
$x + 2 y + 3 z = 4$
$2 x + 3 y + 4 z = 5$
$3 x + 4 y + 5 z = 6$
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 2 & 3 & 4 2 & 4 & 5 \end{matrix} ∣ ∣ ∣ ∣$
$= 1 (15 - 16) - 2 (10 - 12) + 3 (8 - 9)$
$= - 1 - 2 (- 2) + 3 (- 1)$
$= - 1 + 4 - 3$
$= 3 - 3$
$= 0$
$∴$ infinitely many solution

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Similar questions

The system of equations

X+2y+3z=4

2x+3y+4z=5

x + 2 y + 3 z = 4

2 x + 3 y + 4 z = 5

3 x + 4 y + 5 z = 6

The system of equations

X+2y+3z=4

2x+3y+4z=5

2 x + 3 y + 4 z = 16

3 x + 2 y - 5 z = 8

5 x - 6 y + 3 z = 6

3 x + 4 y + 7 z = 4, 2 x - y + 3 z = - 3; x + 2 y - 3 z = 8

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