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

Find the value of k for which following system of equations has a unique solution.

$\begin{matrix} x + 2 y = 3 \\ 5 x + ky + 7 = 0 \end{matrix}$

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 real value except 3

All real value except 5

All real value except 10

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,

\begin{matrix} x + 2 y = 3 \\ 5 x + ky + 7 = 0 \end{matrix}

The equations can be rewritten as,

x + 2 y - 3 = 0

5 x + ky + 7 = 0

Standard system of equations is given as,

\begin{matrix} a_{1} x + b_{1} y + c_{1} = 0 \\ a_{2} x + b_{2} y + c_{2} = 0 \end{matrix}

On comparing this system of equation with given, we gt,

a_{1} = 1, b_{1} = 2, c_{1} = - 3

a_{2} = 3, b_{2} = k, c_{2} = 7

For the unique solution,

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

\frac{1}{5} \neq \frac{2}{k}

1 \times k \neq 2 \times 5

k \neq 10

Hence, except 10, for all real value of k, the system of equation has unique solution.
Option 3 is correct.

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!