Question

(vi) $\frac{x}{8}-\frac{y}{7}=\frac{17}{28};\frac{x}{7}-\frac{y}{8}=1$

Answer 1

$$\begin{gathered} \frac{x}{8}-\frac{y}{7}=\frac{17}{28} \\ \Rightarrow 7x-8y=34...\left(\mathrm{i}\right) \\ \frac{x}{7}-\frac{y}{8}=1 \\ \Rightarrow 8x-7y=56...\left(\mathrm{ii}\right) \\ \mathrm{Adding}\mathrm{eq}.\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\text{we get:} \\ 7x-8y=34 \\ \underline{8x-7y=56} \\ 15x-15y=90 \\ \therefore 15\left(x-y\right)=90 \\ \Rightarrow \left(x-y\right)=6 \\ \mathrm{Subtracting}\mathrm{eq}.\left(\mathrm{ii}\right)\mathrm{from}\left(\mathrm{i}\right),\text{we get:} \\ 7x-8y=34 \\ \underline{8x-7y=56} \\ \underline{\underline{-+-}} \\ -x-y=-22 \\ \therefore -\left(x+y\right)=-22 \\ \therefore \left(x+y\right)=22...\left(\mathrm{iii}\right) \\ \&\left(x-y\right)=6...\left(\mathrm{iv}\right) \\ \mathrm{Adding}\mathrm{eq}.\left(\mathrm{iii}\right)\mathrm{and}\left(\mathrm{iv}\right),\text{we get:} \\ x+y=22 \\ +\underline{x-y=6} \\ 2x=28 \\ \therefore x=14 \\ \mathrm{Substituting}x=14\mathrm{in}\mathrm{eq}.\left(\mathrm{iii}\right),\text{we get:} \\ x+y=22 \\ \Rightarrow 14+y=22 \\ \therefore y=8 \\ \mathrm{Hence},x=14\mathrm{and}y=8\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equations}. \end{gathered}$$