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Classification of Pair of Linear Equations

In the questi...

Question

In the question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion(A): The solution of the pair of linear equations $3 x - 4 y = 7$ and $6 x - 8 y = k$ have infinite number of solution if $k = 14$ .

Reason(R): $a_{1} + b_{1} y + c_{1} = 0$ and $a_{2} + b_{2} y + c_{2} = 0$ have a unique solution if $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ .

Both the assertion (A) and the reason (R) are true, but the reason (R) is not the correct explanation of assertion (A).

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The assertion (A) is false, but the reason (R) is true.

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The assertion (A) is true, but the reason (R) is false.

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

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Solution

The correct option is A
Both the assertion (A) and the reason (R) are true, but the reason (R) is not the correct explanation of assertion (A).

Correct Option is (B)

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Similar questions

3 x - 4 y = 7

6 x - 8 y = k

k = 14

a_{1} x + b_{1} y + c_{1} = 0

a_{2} x + b_{2} y + c_{2} = 0

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

The condition for $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ to be consistent and have a unique solution is

Unique point is obtained for the pair of equations $a_{1}$ x + $b_{1}$ y + $c_{1}$ = 0 and $a_{2}$ x + $b_{2}$ y + $c_{2}$ = 0 if __________ .

3 x + 4 y + 5 = 0

6 x + k y + 9 = 0

k = 8

a_{1} x + b_{1} y + c_{1} = 0

a_{2} x + b_{2} y + c_{2} = 0

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

\sqrt{2} x + \sqrt{3} y = 0, \sqrt{3} x - \sqrt{8} y = 0

a_{1} x + b_{1} y + c_{1} = 0, a_{2} x + b_{2} y + c_{2} = 0

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

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