If the system of linear equations: x + y + 2z = 6 2x + 3y + az = a + 1 – x – 3y + bz = 2b where , has infinitely many solutions, then 7a + 3b is equal to : [2025]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
If the system of linear equations:

x + y + 2z = 6

2x + 3y + az = a + 1

– x – 3y + bz = 2b

where $a, b \in R$ , has infinitely many solutions, then $7 a + 3 b$ is equal to : [2025]

1 16

2 22

3 9

4 12

Ans.
(1)

For infinitely many solutions, we have

$△ =$ $| \begin{matrix} 1 & 1 & 2 \\ 2 & 3 & a \\ - 1 & - 3 & b \end{matrix} |$ $= 0 \Rightarrow 2 a + b - 6 = 0$ ...(i)

Also, $△_{3} =$ $| \begin{matrix} 1 & 1 & 6 \\ 2 & 3 & a + 1 \\ - 1 & - 3 & 2 b \end{matrix} |$ $= 0 \Rightarrow a + b - 8 = 0$ ... (ii)

Solving (i) and (ii), we get a = –2, b = 10

$∴$ 7a + 3b = 7(–2) + 3(10) =16.

Want Us to Email you About Special Offers & Updates?