Question

solve the following system of equations a)1/5x + 1/6y=12,1/3x-3/7y=8 with proper explanation

Answer 1

$$\begin{gathered} \frac{1}{5\mathrm{x}}+\frac{1}{6\mathrm{y}}=12 \\ \mathrm{Let}\frac{1}{\mathrm{x}}=\mathrm{u}\mathrm{and}\frac{1}{\mathrm{y}}=\mathrm{v}. \\ \frac{\mathrm{u}}{5}+\frac{\mathrm{v}}{6}=12 \\ 6\mathrm{u}+5\mathrm{v}=360...\left(1\right) \\ \mathrm{and} \\ \frac{1}{3\mathrm{x}}-\frac{3}{7\mathrm{y}}=8 \\ \frac{\mathrm{u}}{3}-\frac{3\mathrm{v}}{7}=8 \\ \frac{7\mathrm{u}-9\mathrm{v}}{21}=8 \\ 7\mathrm{u}-9\mathrm{v}=168...\left(2\right) \\ \mathrm{From}\mathrm{eqn}\left(1\right),\mathrm{we}\mathrm{get} \\ 6\mathrm{u}=360-5\mathrm{v} \\ \mathrm{u}=\frac{360-5\mathrm{v}}{6} \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{u}\mathrm{in}\left(2\right),\mathrm{we}\mathrm{get} \\ 7\left(\frac{360-5\mathrm{v}}{6}\right)-9\mathrm{v}=168 \\ \frac{250-35\mathrm{v}-54\mathrm{v}}{6}=168 \\ 250-89\mathrm{v}=1008 \\ -89\mathrm{v}=1008-250 \\ -89\mathrm{v}=758 \\ \mathrm{v}=-\frac{758}{89} \\ \mathrm{and} \\ \mathrm{u}=\frac{360-5\left(-\frac{758}{89}\right)}{6}=\frac{32040+3790}{534}=\frac{35830}{534}=\frac{17915}{267} \\ \mathrm{so},\mathrm{x}=\frac{267}{17915}\mathrm{and}\mathrm{y}=-\frac{89}{758}. \end{gathered}$$