If the system of equations x + y + az = b 2x + 5y + 2z = 6 …

Maths Matrices and Determinants JEE Main 2023 - ( Determinats ) Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If the system of equations

x + y + az = b

2x + 5y + 2z = 6

x + 2y + 3z = 3

has infinitely many solutions, then 2a + 3b is equal to

Text Solution

Verified by Experts

The correct answer is:

Given system of equations are

x + y + az = b.....(i)

2x + 5y + 2z = 6.....(ii)

x + 2y + 3z = 3.....(iii)

It is given that the system of equations have infinite solutions.

1(15 - 4)-l(6 - 2)+a(4 - 5)= 0

a = 7

Also, we have

6(15 - 4)-l(18 - 6)+7(12 - 15)= 0

b = 3

a = 7, b = 3

2a + 36= 14 + 9 = 23

Hence, this is the correct option.

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