Question

(i) 13x + 15y = 114; 15x + 13y = 110

Answer 1

$$\begin{gathered} 13x+15y=114....\left(\mathrm{i}\right) \\ 15x+13y=110....\left(\mathrm{ii}\right) \\ \mathrm{Adding}\mathrm{eq}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\text{we get:} \\ 13x+15y=114 \\ \underline{+15x+13y=110} \\ 28x+28y=224 \\ \therefore 28\left(x+y\right)=224 \\ \Rightarrow \left(x+y\right)=8 \\ \mathrm{Subtracting}\mathrm{eq}\left(\mathrm{ii}\right)\mathrm{from}\left(\mathrm{i}\right),\text{we get:} \\ 13x+15y=114 \\ 15x+13y=110 \\ \underline{\underline{---}} \\ -2x+2y=4 \\ \therefore -2\left(x-y\right)=4 \\ \Rightarrow \left(x-y\right)=-2 \\ \therefore \left(x+y\right)=8,\left(x-y\right)=-2 \end{gathered}$$