Question

(v) 17m + 13n = 133; 13m + 17n = 137

Answer 1

$$\begin{gathered} 17m+13n=133....\left(\mathrm{i}\right) \\ 13m+17n=137...\left(\mathrm{ii}\right) \\ \mathrm{Adding}\mathrm{eq}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\text{we get:} \\ 17m+13n=133 \\ \underline{+13m+17n=137} \\ 30m+30n=270 \\ \therefore 30\left(m+n\right)=270 \\ \Rightarrow \left(m+n\right)=9 \\ \mathrm{Subtracting}\mathrm{eq}\left(\mathrm{ii}\right)\mathrm{from}\left(\mathrm{i}\right),\text{we get:} \\ 17m+13n=133 \\ 13m+17n=137 \\ \underline{\underline{---}} \\ 4m-4n=-4 \\ \therefore 4\left(m-n\right)=-4 \\ \Rightarrow \left(m-n\right)=-1 \\ \therefore \left(m+n\right)=9,\left(m-n\right)=-1 \end{gathered}$$