Question

Find the value of k for which the pair of linear equation x+2y-5=0 and 5x+6y+k=0,represent coincident lines ​

Answer 1

Answer:

coincident lines =

=a1/a2=b1/b2=c1/c2

so

1/5=2/6=-5/k

1/5=-5/k

k=-25

Answer 2

No value of k can make the pair of equations to represent coincident lines.

• Now to become coincident lines the necessary condition is that the slopes of two lines must be equal.
• The given equations of straight lines are x+2y-5=0 and 5x+6y+k=0. Now the slope of the first line is $-\frac{1}{2}$ and the slope of the second line is $-\frac{5}6}$ . So they are not same.
• Moreover if we apply the condition of coincidence of two lines that is $\frac{1}{5} =\frac{2}{6} =\frac{-5}{k}$
• This gives us two values of k that is k= -15 and k = -25. But both are not same and generates two straight lines which intersects the first one.
• So there is no value of k which can make the given pair of equations of straight lines to represent coincident straight lines.