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Pair of Linear Equations in Two variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsPair of Linear Equations in Two variables1 Mark
MCQ
Statement A (Assertion) : The system of equations $x+y-6=0$ and $x-y-2=0$ has a unique solution.
Statement R (Reason): The system of equations $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ has a unique solution when $\frac{a_1}{a_2}=\frac{b_1}{b_2}$.
  • A
    (a) Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
  • B
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
  • ✓
    Assertion (A) is true but reason ( $R$ ) is false.
  • D
    Assertion $(A)$ is false but reason $(R)$ is true.
✓

Answer

Correct option: C.
Assertion (A) is true but reason ( $R$ ) is false.
(c) : The given system of equations is
$x+y-6=0$ and $x-y-2=0$
Here, $\frac{a_1}{a_2}=\frac{1}{1}=1, \frac{b_1}{b_2}=\frac{1}{-1}=-1, \frac{c_1}{c_2}=\frac{-6}{-2}=3$
Since, $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$
$\therefore \quad$ The given system of equations has a unique solution.
So, Assertion is true but Reason is false.

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