AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

For which value of $α$ , equations $αx + 3 y = α - 3$ and $12 x + αy = α$ has a unique solution?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

All value of

α

(except 4 and -4)

All value of

α

(except 6 and -6)

All value of

α

(except 2 and -2)

All value of

α

(except 3 and -3)

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

It is given the system of linear equation is,

αx + 3 y = α - 3 . . . . (1)

and

12 x + αy = α . . . . (2)

Now let consider the system of equations,

a_{1} x + b_{1} y + c_{1} = 0

…..(3)

a_{2} x {+ b}_{2} y + c_{2} = 0

……(4).
For a unique solution of equations (3) and (4) we must have,

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

Now comparing (3) with (1) and (4) with (2) we get,

a_{1} = α

b_{1} = 3

, and

c_{1} = - (α - 3)

and

a_{2} = 12

b_{2} = α

c_{2} = - α

For a unique solution, we must have,

\frac{α}{12} \neq \frac{3}{α}

\Rightarrow α^{2} \neq 36

\Rightarrow α \neq 6 or - 6

Hence, for all values of

α

except

6

and

- 6

the system has a unique solution.
The given pair of linear equations has a unique solution.
So the correct option is 2.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

best study material, now at your finger tips!

live classes
progress tracking
24x7 mentored guidance
study plan analysis

download the app

For which value of α , equations αx+3y=α-3 and 12x+αy=α has a unique solution?

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App

For which value of $α$ , equations $αx + 3 y = α - 3$ and $12 x + αy = α$ has a unique solution?