The system kx - y = 2 and 6x - 2y = 3 has a unique solution only …

MCQ

The system $kx - y = 2$ and $6x - 2y = 3$ has a unique solution only when:

A
$\text{k}=-6,$
B
$\text{k}\neq-6$
C
$\text{k}=0$
✓
$\text{k}\neq3$

✓

Answer

Correct option: D.

$\text{k}\neq3$

$kx - y = 2$ and $6x - 2y = 3$
We know that,
the system of linear equations $a_1 x+b_1 y+c_1=0, a_2 x+b_2 y+c_2=0$ has a unique solution if $\frac{\text{a}_1}{\text{a}_2}\neq\frac{\text{b}_1}{\text{b}_2}.$
So, $\frac{\text{k}}{6}\neq\frac{-1}{-2}$
$\Rightarrow\text{k}\neq3.$

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