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

If $a m ≠ b l,$ then the system of equations, $a x + b y = c, l x + m y = n$ then the system of equations, have

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

no solution

infinitely many solutions

unique solution

None

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given equations are

a x + b y = c, l x + m y = n

.
We know that, to say a pair of linear equations of the form

a 1 x + b 1 y + c 1 = 0

and

a 2 x + b 2 y + c 2 = 0

are having unique solutions, the ratio of the coefficients should be

a 1 a 2 ≠ b 1 b 2

.
On comparing the above equations with

a 1 x + b 1 y + c 1 = 0

and

a 2 x + b 2 y + c 2 = 0

, we get

a 1 = a, b 1 = b, c 1 = − c

and

a 2 = l, b 2 = m, c 2 = − n

.
Also given that

a m ≠ b l,

⇒ a l ≠ b m

⇒ a 1 a 2 ≠ b 1 b 2

For a pair of equations with no solution, it must satisfy

a 1 a 2 ≠ b 1 b 2

.
So, the given system of equations has unique solution, if

a m ≠ b l .

The correct option is (3).

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!