Question

. For what value of k,the pair of linear equations 4x + 2y= -7
and kx + 5y = 8 have no solution.

please answer the question ...

urjent​

Answer 1

ᏟϴᎡᎡᎬᏟͲ ϘႮᎬՏͲᏆϴΝ:-

For what value of k,the pair of linear equations 4x + 2y= -7 and kx + 5y = 8 have infinite solution.

ᎪΝՏᏔᎬᎡ:-

The given system of equations is:

8x + 5y – 9 = 0

kx + 10y – 18 = 0

The above equations are of the form

a1 x + b1 y − c1 = 0

a2 x + b2 y − c2 = 0

Here, a1 = 8, b1 = 5,

c1 = -9 a2 = k,

b2 = 10, c2 = -18

So according to the question,

For unique solution, the condition is

a1/a2 = b1/b2 = c1/c2

8/k=5/10 = −9/−18 = 1/2

⇒ k = 16

Hence, the given system of equations will have infinitely many solutions, if k = 16.

Answer 2

Find the value of k for the system of equations having infinitely many solution: 8x + 5y = 9; kx + 10y = 18

Answer

The given system of equations is:

8x + 5y – 9 = 0

kx + 10y – 18 = 0

The above equations are of the form

a1 x + b1 y − c1 = 0

a2 x + b2 y − c2 = 0

Here, a1 = 8, b1 = 5, c1 = -9

a2 = k, b2 = 10, c2 = -18

So according to the question, For unique solution, the condition is

a1/a2 = b1/b2 =c1/c2

8/k = 5/10 = -9/-18 = 1/2

⇒ k = 16

Hence, the given system of equations will have infinitely many solutions, if k=16.