Statement A (Assertion) : The system of equations are inconsisten… - Vidyadip

MCQ

Statement $A\ ($Assertion$)$ : The system of equations are inconsistent: $2 x+4 y=10$
$3 x+6 y=12$
Statement $R\ ($Reason$) : A$ pair of linear equations which has no solution is called an inconsistent pair of linear equations.

✓
$(a)$ 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 $(A)$.
C
Assertion $(A)$ is true but reason $(R)$ is false.
D
Assertion $(A)$ is false but reason $(R)$ is true.

✓

Answer

Correct option: A.

$(a)$ Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.

The given system of equations can be written as $2 x+4 y-10=0,$
$3 x+6 y-12=0$
Here, $\frac{a_1}{a_2}=\frac{2}{3}, \frac{b_1}{b_2}$
$=\frac{4}{6}=\frac{2}{3}, \frac{c_1}{c_2}$
$=\frac{-10}{-12}=\frac{5}{6}$
Clearly, $\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.
So, the given system of equations has no solution, i.e., it is inconsistent.
$\therefore $ So, Assertion and Reason both are true and Reason is the correct explanation of Assertion.

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