Question

(i) 12x + 17y = 53; 17x + 12y = 63

Answer 1

$$\begin{gathered} 12x+17y=53....\left(\mathrm{i}\right) \\ 17x+12y=63...\left(\mathrm{ii}\right) \\ \mathrm{Adding}\mathrm{eq}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\text{we get:} \\ 12x+17y=53 \\ \underline{+17x+12y=63} \\ 29x+29y=116 \\ \therefore 29\left(x+y\right)=116 \\ \Rightarrow \left(x+y\right)=4 \\ \mathrm{Subtracting}\mathrm{eq}\left(\mathrm{ii}\right)\mathrm{from}\left(\mathrm{i}\right),\text{we get:} \\ 12x+17y=53 \\ 17x+12y=63 \\ \underline{\underline{---}} \\ -5x+5y=-10 \\ \therefore -5\left(x-y\right)=-10 \\ \Rightarrow \left(x-y\right)=2 \\ \therefore \left(x+y\right)=4...\left(\mathrm{iii}\right) \\ \therefore \left(x-y\right)=2...\left(\mathrm{iv}\right) \\ \mathrm{Adding}\mathrm{eq}\left(\mathrm{iii}\right)\mathrm{and}\left(\mathrm{iv}\right),\text{we get:} \\ x+y=4 \\ +\underline{x-y=2} \\ 2x=6 \\ \therefore x=3 \\ \mathrm{Substituting}x=3\mathrm{in}\mathrm{eq}\left(\mathrm{iii}\right),\text{we get:} \\ x+y=4 \\ \Rightarrow 3+y=4 \\ \therefore y=1 \\ \mathrm{Hence},x=3\text{and}y=1\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equations}. \end{gathered}$$