For which of the following ordered pairs (μ, δ), the system of linear equations x + 2y + 3z = 1 3x + 4y + 5z = μ 4x + 4y + 4z = δ is inconsistent ?

Question

For which of the following ordered pairs (μ, δ), the system of linear equations x + 2y + 3z = 1 3x + 4y + 5z = μ 4x + 4y + 4z = δ is inconsistent ? (A) (4, 6) (B) (3, 4) (C) (4, 3) (D) (1, 0)

Tardigrade Admin · Accepted Answer

2 × (ii) - 2 × (i) - (iii): - 0=2μ-2-δ ⇒ δ=2(μ-1)

Q. For which of the following ordered pairs $(μ, δ),$ the system of linear equations
$x + 2 y + 3 z = 1$
$3 x + 4 y + 5 z = μ$
$4 x + 4 y + 4 z = δ$
is inconsistent ?

(4, 6)

(3, 4)

(4, 3)

(1, 0)

$2 \times (ii) - 2 \times (i) - (iii) : -$
$0 = 2 μ - 2 - δ$
$\Rightarrow δ = 2 (μ - 1)$

Q. For which of the following ordered pairs (μ,δ), the system of linear equations x+2y+3z=1 3x+4y+5z=μ 4x+4y+4z=δ is inconsistent ?