Question

(ii) 25x − 24y = 197; 24y − 25y = 195

Answer 1

$$\begin{gathered} 25x-24y=197....\left(\mathrm{i}\right) \\ 24x-25y=195...\left(\mathrm{ii}\right) \\ \mathrm{Adding}\mathrm{eq}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\text{we get:} \\ 25x-24y=197 \\ \underline{+24x-25y=195} \\ 49x-49y=392 \\ \therefore 49\left(x-y\right)=392 \\ \Rightarrow \left(x-y\right)=8 \\ \mathrm{Subtracting}\mathrm{eq}\left(\mathrm{ii}\right)\mathrm{from}\left(\mathrm{i}\right),\text{we get:} \\ 25x-24y=197 \\ 24x-25y=195 \\ \underline{\underline{-+-}} \\ x+y=2 \\ \therefore \left(x+y\right)=2 \\ \therefore \left(x+y\right)=2...\left(\mathrm{iii}\right) \\ \therefore \left(x-y\right)=8...\left(\mathrm{iv}\right) \\ \mathrm{Adding}\mathrm{eq}\left(\mathrm{iii}\right)\mathrm{and}\left(\mathrm{iv}\right),\text{we get}: \\ x+y=2 \\ +\underline{x-y=8} \\ 2x=10 \\ \therefore x=5 \\ \mathrm{Substituting}x=5\mathrm{in}\mathrm{eq}\left(\mathrm{iii}\right),\text{we get:} \\ x+y=2 \\ \Rightarrow 5+y=2 \\ \therefore y=-3 \\ \mathrm{Hence},x=5\mathrm{and}y=-3\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equations}. \end{gathered}$$