Question

Given equations are ( x+5 y-7=0 ) and ( 4 x+20 y+k=0 )
Here, ( a_{1}=1, quad b_{1}=5, quad c_{1}=-7 )
[
a_{2}=4, quad b_{2}=20, quad c_{2}=k
]
We know that equations represent coincident lines if they are consistent with many solutions.
( frac{a_{1}}{a_{2}}=frac{b_{1}}{b_{2}}=frac{c_{1}}{c_{2}} Rightarrow frac{1}{4}=frac{5}{20}=frac{-7}{k} Rightarrow frac{1}{4}=frac{-7}{k} Rightarrow k=-28 )
Hence, for ( k=-28 ), given equations represent coincident
lines.

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

Solution