Question

find the value of k for which pair of equations 2x+ky=1 and 3x-5y=7 has no solution

Answer 1

2x+ky=1
3x-5y=7

2x+ky-1
3x-5y-7

Compare these solution. A1/A2 ,B1/B2,C1/C2


A1/A2=2/3
B1/B2=k/-5 or -k/5(- goes to numerator from denominator)
C1/C2=-1/-7

If the equations are no solution

A1/A2=B1/B2≠C1/C2
2/3=K/-5≠C1/C2

Compare B1/B2 with C1/C2

-k/5≠-1/-7

Cross Multiply

-7(-k)≠-1(5)

7k≠-5

k≠-5/7 (Answer)

Answer 2

For what value of k the system
2x+ky=1
3x-5y=7
will have
(i)unique solution
(ii)no solution.
Is there a value of k for which the system has infinitely many solutions?