Question

for what value of k the following equations have no solution 6x +4y+k=0 3x+2y+ 5= 0

Answer 1

If the equation have no solution then the line made by them will be parallel to each other.

For having no solution the condition is :-

$\frac{a1}{a2} = \frac{b1}{b2} is \: not \: equal \: to \: \frac{c1}{c2}$


Here ,

a1 = 6. b1 = 4. c1 = k

a2 = 3 b2 = 2 c2 = 5


$\frac{a1}{a2} is \: not \: equalto = \frac{c1}{c2}$

6/3 ≠ k / 5

2 ≠ k /5

10 ≠ k

So, for any value of k except 10 will the equation have no solution !!

Answer 2

a1 = 6 , a2 = 3 , b1 = 4 + k , b2 = 2 + 5
for no sol. , a1/ a2 is not equal to b1 / b2
6 / 3 is not equal to 4 + k / 2 + 5
2 =\ 4 + k / 7
cross multiply, 14 =\ 4 + k
hope it helps u !!!!
10 =\ k
so , there fore k is not equal to 10