Question

Solve the following equation and verify your answer:

\[\frac{y - (7 - 8y)}{9y - (3 + 4y)} = \frac{2}{3}\]

Answer 1

\[\frac{y - (7 - 8y)}{9y - (3 + 4y)} = \frac{2}{3}\]

\[\text{ or }\frac{9y - 7}{5y - 3} = \frac{2}{3}\]

\[\text{ or }27y - 21 = 10y - 6 [\text{ After cross multiplication }]\]

\[\text{ or }27y - 10y = - 6 + 21\]

\[\text{ or }17y = 15\]

\[\text{ or }y = \frac{15}{17}\]

\[\text{ Thus, }y = \frac{15}{17}\text{ is the solution of the given equation . }\]

\[\text{ Check: }\]

\[\text{ Substituting }y = \frac{15}{17}\text{ in the given equation, we get: }\]

\[\text{ L . H . S . }= \frac{9(\frac{15}{17}) - 7}{5(\frac{15}{17}) - 3} = \frac{135 - 119}{75 - 51} = \frac{16}{24} = \frac{2}{3}\]

\[\text{ R . H . S .} = \frac{2}{3}\]

\[ \therefore\text{ L . H . S . = R . H . S . for }y = \frac{15}{17}\]