Question

If the equation 6 x - 5 Y + 11 =0 and 15 X + k y - 9 = 0 have no solution then the value of k is

Answer 1

Given Equation is 6x - 5y + 11 = 0

Here, a1 = 6, b1 = -5, c1 = 11  

Given Equation is 15x + ky - 9 = 0.

here, a2 = 15, b2 = k, c2 = -9.

Given that the equation has no solution.

⇒ a1/a2 = b1/b2 ≠ c1/c2

⇒ (6/15) = (-5/k)

⇒ 6k = -75

⇒ k = -75/6

⇒ k = -25/2.

Therefore, the value of k = -25/2.

Hope this helps!

Answer 2

$\mathbb{\huge{ANSWER - }}$

$\mathbb{METHOD \:OF\: \: SOLUTION:-}$

For No Solution we have must be;

$\bold{ \frac{a1}{a2} = \frac{b1}{b2} ≠{ \frac{c1}{c2}}}$

Here,

a1=6

a2=15

b1=-5

b2=k

c1=11

c2=9

Now,

Substitute the value of in Equation:-

$\bold{ \frac{6}{15} = \frac{5}{k}}$=

$\frac{6}{15} = \frac{5}{k} \\ \\ 6k = 15\times- 5 \\ \\ k = \frac{15 \times -5}{ \1} \\ \\ \\ k = -25/3$