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Linear Equation In Two Variable — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsLinear Equation In Two Variable1 Mark
MCQ
The system $x - 2y = 3$ and $3x + ky = 1$ has a unique solution only when:
  • A
    $\text{k}=-6,$
     
  • ✓
    $\text{k}\neq-6$
     
  • C
    $\text{k}=0$
     
  • D
    $\text{k}\neq0$
✓

Answer

Correct option: B.
$\text{k}\neq-6$
 
$x - 2y = 3$ and $3x + ky = 1$
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, $\frac{1}{3}\neq\frac{-2}{\text{k}}$
$\Rightarrow\text{k}\neq-6.$

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