Question

Solve the following equation and verify your answer:

\[\frac{1 - 9y}{19 - 3y} = \frac{5}{8}\]

Answer 1

\[\frac{1 - 9y}{19 - 3y} = \frac{5}{8}\]

\[\text{ or }8 - 72y = 95 - 15y [\text{ After cross multiplication }]\]

\[\text{ or }95 - 15y = 8 - 72y \]

\[\text{ or }72y - 15y = 8 - 95\]

\[\text{ or }57y = - 87\]

\[\text{ or }y = \frac{- 87}{57}\]

\[\text{ or }y = \frac{- 29}{19}\]

\[\text{ Thus }y = \frac{- 29}{19}\text{ is the solution of the given equation . }\]

\[\text{ Check: }\]

\[\text{ Substituting }y = \frac{- 29}{19}\text{ in the given equation, we get: }\]

\[\text{ L . H . S . }= \frac{1 - 9(\frac{- 29}{19})}{19 - 3(\frac{- 29}{19})} = \frac{19 + 261}{361 + 87} = \frac{280}{448} = \frac{5}{8}\]

\[\text{ R . H . S . }= \frac{5}{8}\]

\[ \therefore\text{ L . H . S . = R . H . S . for }y = \frac{- 29}{19}\]