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