Sample Question 2: Do the equations \(4x + 3y - 1 = 5\) and \(12x + 9y = 15\) represent a pair of coincident lines? Justify your answer.
No.
Rewrite the first equation.
\(4x + 3y - 1 = 5\)
\(4x + 3y = 6\)
The second equation is \(12x + 9y = 15\).
Compute the three ratios.
\(\dfrac{a_1}{a_2} = \dfrac{4}{12} = \dfrac{1}{3}\)
\(\dfrac{b_1}{b_2} = \dfrac{3}{9} = \dfrac{1}{3}\)
\(\dfrac{c_1}{c_2} = \dfrac{6}{15} = \dfrac{2}{5}\)
The constants ratio is different, so the lines are parallel distinct lines.
Hence, they are not coincident.