Question

# For what value of k will the equations x + 5y-7= 0 and 4x + 20y + k=0 represent coincident lines?

Solution

Given equations are
x +5y– 7 = 0 and 4x + 20y+k = 0
Here, d=1, b = 5 , 9 = -7
a2 = 4 , b2 = 20, C2 = k
We know that equations represent coincident lines if they
are consistent with many solutions.
1 -7
a1_b_
9 1 -5--7
d2 62 C24 20k
Hence, for k = -28, given equations represent coincident
lines.
[
k= -28