Question

Find the value of k for which the following system of equations has no solution:
kx-5y=26x+2y=7

Answer 1

k = -15

Step-by-step explanation:

Given:  

kx -5y = 2

6x + 2y = 7

The system of equations has no solution.

So a1/a2 = b1/b2 but not equal to c1/c2

a1 = k, b1 = -5, c1 = 2

a2 = 6, b2 = 2, c2 = 7

 So  a1/a2 = b1/b2

k/ 6 = -5/ 2

2k = -5 * 6

2k = -30

k = -30/2

Therefore k = -15 which is not equal to 2/7.

Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

We know the case of no solution

$\Large{\star{\boxed{\rm{\frac{a_1}{a_2} = \frac{b_1}{b_2} ≠ \frac{c_1}{c_2}}}}}$

Where,

a1 = k, a2 = 6

b1 = -5, b2 = 2

c1 = 2, c2 = 7

_____________[Put Values]

$\tt{→\frac{k}{6} = \frac{-5}{2} ≠ \frac{2}{7}} \\ \\ \sf{→\frac{k}{6} = \frac{-5}{2}} \\ \\ \sf{→ k = \frac{-5 \times \cancel{6}}{\cancel{2}}} \\ \\ \sf{→k = -5 \times 3} \\ \\ \sf{→k = -15} \\ \\ \Large{\star{\boxed{\rm{k = -15}}}}$