For a real number a, if the system of linear equations, ha…

Maths JEE - Advanced Previous Year Paper JEE-Advanced-2017-Paper-1 Numeric Response

Published by: CGP EDU Academic Team

Published on: August 13, 2026

For a real number a, if the system

of linear equations, has infinitely many solutions, then

Text Solution

Verified by Experts

The correct answer is:

(1)

Here,

which gives = - 1 or +1

For a = 1, the equations become

x+y+z=1

x + y+z = -l

and x + y + z = 1

which give no solution

For a = -1, the equations become

x-y + z = 1

-x + y - z = -1

x-y + z = 1

which are all same and hence infinitely many solutions

Hence, a = -1

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