Question

Find the value of k so equations x+2y= -7,
2x+ky+14= 0 will be coincident.

Answer 1

x + 2y = -7    (1) 
2x + ky = -14  (2) 
multiply equ (1) by 2 we get , 
2x + 4y = -14 
2x + ky = -14  ( subtract the equations)
...................
4y - ky = 0 
y ( 4 - k) = 0 
y = 0; 4 - k = 0 
y = 0 ; k = 4  
apply y values in equ (1) we get 
x + 2 (0) = -7 
x = - 7 
x = -7,  y =0 , k = 4 

Answer 2

x + 2y = -7
⇒ x + 2y + 7 = 0
2x + ky + 14 = 0

These two are coincident.

$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} \\\\ \frac{1}{2} = \frac{2}{k} = \frac{7}{14} \\ \\k=2 \times 2=4$

So, k is 4.