The system of equations 3x + y - z = 0 5x + 2y - 3z = 2 15x + 6y - 9z = 5 has

Question

The system of equations 3x + y - z = 0 5x + 2y - 3z = 2 15x + 6y - 9z = 5 has (A) a unique solution (B) two distinct solutions (C) no solution (D) infinitely many solutions

Tardigrade Admin · Accepted Answer

Δ = |3&1&-1 5&2&-3 15&6&-9|=3|3&1&-1 5&2&-3 5&6&-3|=0 and ∴ 3 (5x + 2y - 3z) = 6 i.e., 15 x + 6 y - 9 z = 6 Also, 15x + 6 y - 9 z = 5 and 6 ≠ 5 ∴ the system has no solution.

Q. The system of equations $3 x + y - z = 0$
$5 x + 2 y - 3 z = 2$
$15 x + 6 y - 9 z = 5$ has

a unique solution

two distinct solutions

no solution

infinitely many solutions

$Δ = ∣ ∣ 3515126 - 1 - 3 - 9 ∣ ∣ = 3 ∣ ∣ 355126 - 1 - 3 - 3 ∣ ∣ = 0$
and $∴ 3 (5 x + 2 y - 3 z) = 6$
$i . e ., 15 x + 6 y - 9 z = 6$
Also, $15 x + 6 y - 9 z = 5$ and $6 \neq = 5$
$∴$ the system has no solution.

Q. The system of equations 3x+y−z=0 5x+2y−3z=2 15x+6y−9z=5 has