Question

Assertion: The value of k for which the system of linear equations 3x-4y=7 and 6x-8y=k have infinite number of solution is 14.
Reason: The graph of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 gives a pair of intersecting lines if a1/a2 ≠ b1/b2.

(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Itz difficult (ᗒᗩᗕ)​

Answer 1

Answer:

(c) A is true but R is false.

Explanation:

Assertion:

Two equations are,

• 3x - 4y = 7
• 6x - 8y = k

We can write them as,

• 3x - 4y - 7 = 0
• 6x - 8y - k = 0

Here,

If $\rm a_1 : a_2 = b_1 : b_2 = c_1 : c_2$ then it has infinitely many solutions.

Let's check,

$\implies \rm \dfrac{a_1}{a_2} = \dfrac{3}{6} = \dfrac{1}{2}$

$\implies \rm \dfrac{b_1}{b_2} = \dfrac{4}{8} = \dfrac{1}{2}$

$\implies \rm\dfrac{c_1}{c_2} = \dfrac{7}{k} = \dfrac{7}{14} = \dfrac{1}{2} \:\:\:\:[\because k = 14]$

$\rm \therefore a_1 : a_2 = b_1 : b_2 = c_1 : c_2$

Hence, Assertion is True.

Reason:

The graph of linear equations$\rm a_1x+b_1y+c_1=0$ and $\rm a_2x+b_2y+c_2=0$ gives a pair of intersecting lines if $\rm \dfrac{a_1}{a_2} \neq \dfrac{ b_1}{b_2}$

The reason for the assertion is false.

Because when, $\rm a_1 : a_2 \neq b_1 : b_2$ it's consistent with exactly one solution.

Hence, the reason is incorrect.

__________________________

Answer 2

Answer:

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