n (A): The system of linear equations

Question

Assertion (A): The system of linear equations 2x + 3y = 7 and kx + 9/2 y = 12 have no solution, if k = 3.
Reason (R): The system of linear equations $a ₁ x + b ₁ y + c ₁ = 0 a n d a ₂ x + b ₂ y + c ₂ = 0$ have no solution, if $a ₁ / a ₂ = b ₁ / b ₂ .$

Smart Achievers · Accepted Answer

(3)

Rationale: The system of linear equations in Reason (R) have no solution, if
$a ₁ / a ₂ = b ₁ / b ₂ \neq c ₁ / c ₂ .$ .
So, Reason (R) is false. The system of linear equations in Assertion (A) will have no solution if
k/2 = 9/3 ≠ 12/7 or k/2 = 3/2 ≠ 12/7 or k = 3.

Solution

Q.
Assertion (A): The system of linear equations 2x + 3y = 7 and kx + 9/2 y = 12 have no solution, if k = 3.
Reason (R): The system of linear equations $a ₁ x + b ₁ y + c ₁ = 0 a n d a ₂ x + b ₂ y + c ₂ = 0$ have no solution, if $a ₁ / a ₂ = b ₁ / b ₂ .$

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

Ans.
(3)

Rationale: The system of linear equations in Reason (R) have no solution, if
$a ₁ / a ₂ = b ₁ / b ₂ \neq c ₁ / c ₂ .$ .
So, Reason (R) is false. The system of linear equations in Assertion (A) will have no solution if
k/2 = 9/3 ≠ 12/7 or k/2 = 3/2 ≠ 12/7 or k = 3.

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