Question

Solve the following equation and verify your answer:
$\frac{1-9y}{19-3y}=\frac{5}{8}$

Answer 1

$$\begin{gathered} \frac{1-9\mathrm{y}}{19-3\mathrm{y}}=\frac{5}{8} \\ \mathrm{or}8-72\mathrm{y}=95-15\mathrm{y}[\text{After c}\mathrm{ross}\mathrm{multipl}\text{ication}] \\ \mathrm{or}95-15\mathrm{y}=8-72\mathrm{y} \\ \mathrm{or}72\mathrm{y}-15\mathrm{y}=8-95 \\ \mathrm{or}57\mathrm{y}=-87 \\ \mathrm{or}\mathrm{y}=\frac{-87}{57} \\ \mathrm{or}\mathrm{y}=\frac{-29}{19} \\ \mathrm{Thus}\mathrm{y}=\frac{-29}{19}\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{y}=\frac{-29}{19}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{1-9\left({\displaystyle \frac{-29}{19}}\right)}{19-3\left({\displaystyle \frac{-29}{19}}\right)}=\frac{19+261}{361+87}=\frac{280}{448}=\frac{5}{8} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{5}{8} \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{y}=\frac{-29}{19} \end{gathered}$$