Question

Assertion (A): (2x − 3у, 8) = (2, x + 2y) ⇒ x = 1 and y = −2.

Reason (R): 2x − 3y = 2 and 8 = x + 2y which on solving give x = 4 and y = 2.

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is false, R is true.

Explanation:

Solving the system of linear equations from Reason R: 2x − 3у = 2 and x + 2y = 8. From the second equation, x = 8 − 2y. Substituting this into the first equation:

2(8 − 2y) − 3y = 2

16 − 4y − 3y = 2

7y = 14

y = 2, and

x = 8 − 2(2) = 4

Thus, x = 4 and y = 2, making Reason R true. Assertion A states x = 1 and y = −2, which is false.