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

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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.

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