Question

For what value of K the pair of equations Kx+2y=5,3x-4y=10 has no solution.

Answer 1

if a1/a2=b1/b2 not equal to c1/c2 then it will have no Sol.
here, k/3=2/-4
-4k=6
-k=6/4
k=-3/2

Answer 2

Answer:

The value of K is $K=-\frac{3}{2}$  and $K\neq\frac{3}{2}$

Step-by-step explanation:

Given : Equation $Kx+2y=5,3x-4y=10$

To find : For what value of K the pair of equations has no solution ?

Solution :  

When the system of equation is in form $ax+by+c=0, dx+ey+f=0$ then the condition for no solutions is  

$\frac{a}{d}=\frac{b}{e}\neq \frac{c}{f}$

Comparing the value are a=K,b=2, c=-5 , d=3, e=-4, f=-10

Substituting the values,

$\frac{K}{3}=\frac{2}{-4}\neq \frac{-5}{-10}$

$\frac{K}{3}=-\frac{1}{2}\neq \frac{1}{2}$

Taking 1, $\frac{K}{3}=-\frac{1}{2}$

$2\times K=-1\times 3$

$2K=-3$

$k=-\frac{3}{2}$

Taking 2, $\frac{K}{3}\neq \frac{1}{2}$

$2\times K\neq1\times 3$

$2K\neq3$

$K\neq\frac{3}{2}$

Therefore, The value of K is $K=-\frac{3}{2}$  and $K\neq\frac{3}{2}$