Question

Solve the following equation and verify your answer:
$\frac{y-(7-8y)}{9y-(3+4y)}=\frac{2}{3}$

Answer 1

$$\begin{gathered} \frac{\mathrm{y}-(7-8\mathrm{y})}{9\mathrm{y}-(3+4\mathrm{y})}=\frac{2}{3} \\ \mathrm{or}\frac{9\mathrm{y}-7}{5\mathrm{y}-3}=\frac{2}{3} \\ \text{or}27\mathrm{y}-21=10\mathrm{y}-6\text{[After c}\mathrm{ross}\mathrm{multipl}\text{ication}] \\ \mathrm{or}27\mathrm{y}-10\mathrm{y}=-6+21 \\ \mathrm{or}17\mathrm{y}=15 \\ \mathrm{or}\mathrm{y}=\frac{15}{17} \\ \mathrm{Thus},\mathrm{y}=\frac{15}{17}\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{y}=\frac{15}{17}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{9\left({\displaystyle \frac{15}{17}}\right)-7}{5\left({\displaystyle \frac{15}{17}}\right)-3}=\frac{135-119}{75-51}=\frac{16}{24}=\frac{2}{3} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{2}{3} \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{y}=\frac{15}{17} \end{gathered}$$