Question

For what value of k, the following system of equations will represent the coincident lines?

x + 2y + 7 = 0

2x + ky + 14 = 0

Answer 1

The given system of equations may be written as

x + 2y + 7 = 0

2x + ky + 14 = 0

The given system of equations is of the form

`a_1x + b_1y + c_1 = 0`

`a_2x + b_2y + c_2 = 0`

Where `a_1 = 1, b_1 = 2, c_1 = 7`

And `a_2 = 2,b_2 = k, c_2 = 14`

The given equations will represent coincident lines if they have infinitely many solutions,

The condition for which is

`a_1/a_2 = b_1/b_2 = c_1/c_2 =. 1/2 = 2/k = 7/14 => k = 4`

Hence, the given system of equations will represent coincident lines, if  k = 4