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Question
Solve the following equation and verify your answer:
\[\frac{y - (7 - 8y)}{9y - (3 + 4y)} = \frac{2}{3}\]
Sum
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Solution
\[\frac{y - (7 - 8y)}{9y - (3 + 4y)} = \frac{2}{3}\]
\[\text{ or }\frac{9y - 7}{5y - 3} = \frac{2}{3}\]
\[\text{ or }27y - 21 = 10y - 6 [\text{ After cross multiplication }]\]
\[\text{ or }27y - 10y = - 6 + 21\]
\[\text{ or }17y = 15\]
\[\text{ or }y = \frac{15}{17}\]
\[\text{ Thus, }y = \frac{15}{17}\text{ is the solution of the given equation . }\]
\[\text{ Check: }\]
\[\text{ Substituting }y = \frac{15}{17}\text{ in the given equation, we get: }\]
\[\text{ L . H . S . }= \frac{9(\frac{15}{17}) - 7}{5(\frac{15}{17}) - 3} = \frac{135 - 119}{75 - 51} = \frac{16}{24} = \frac{2}{3}\]
\[\text{ R . H . S .} = \frac{2}{3}\]
\[ \therefore\text{ L . H . S . = R . H . S . for }y = \frac{15}{17}\]
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