Question

What is the value of k, for which the simultaneous equations 2x+3y=8 and 6x-ky=24 have infinitely many solutions? What is the value of k, for which the simultaneous equations 2x+3y=8 and 6x-ky=24 have infinitely many solutions

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given,

Equation of line 1: 2x + 3y = 8

Equation of line 2: 6x - ky = 24

The given equations have infinitely many solutions

To Find,

The value of k =?

Solution,

In the case of equations having infinitely many solutions, we know that

a1/a2 = b1/b2 = c1/c2 ⇒ Equation 1

In the equation 1,

2x + 3y = 8

2x + 3y - 8 = 0

Therefore, a1 = 2, b1 = 3 and c1 = -8

Similarly, in the equation 2,

6x - ky = 24

6x - ky - 24 =0

Therefore, a2 = 6, b2 = -k and c2 = -24

Equating values in the eqaution 1,

2 / 6 = 3/ -k = -8 / -24

1 / 3 = 3 / -k  = 1/3

3 / -k = 1 / 3

By cross-multipying, we have

-k = 9

k = -9

Hence, the value of k, for which the simultaneous equations 2x+3y=8 and 6x-ky=24 have infinitely many solutions is -9.