Statement A (Assertion) : The pair of linear equations 2 x-y-5=0 … - Vidyadip

MCQ

Statement $A \ ($Assertion$)$ : The pair of linear equations $2 x-y-5=0$ and $x-y-3=0$ represent intersecting lines.
Statement $R\ ($Reason$)$ : The linear equations $2 x-y-5=0$ and $x-y-3=0$ meet the $y-$ axis at $(0,-5)$ and $(0,3)$ respectively.

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.

The given system of linear equations is
$2 x-y-5=0 \ldots(i)$
$x-y-3=0\ldots(ii)$
Now, $\frac{a_1}{a_2}=\frac{2}{1}, \frac{b_1}{b_2}$
$=\frac{-1}{-1}=1, \frac{c_1}{c_2}$
$=\frac{-5}{-3}=\frac{5}{3}$
So, given equations represent intersecting lines.
$(0,-5)$ satisfy equation $(i)$ but $(0,3)$ does not satisfy equation $(ii)$.
So, Assertion is true but Reason is false.

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