Question

(iv) 15x − 12y = 69; 12x − 15y = 39

Answer 1

$$\begin{gathered} 15x-12y=69....\left(\mathrm{i}\right) \\ 12x-15y=39...\left(\mathrm{ii}\right) \\ \mathrm{Adding}\mathrm{eq}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\text{we get}: \\ 15x-12y=69 \\ \underline{+12x-15y=39} \\ 27x-27y=108 \\ \therefore 27\left(x-y\right)=108 \\ \Rightarrow \left(x-y\right)=4 \\ \mathrm{Subtracting}\mathrm{eq}\left(\mathrm{ii}\right)\mathrm{from}\left(\mathrm{i}\right),\text{we get}: \\ 15x-12y=69 \\ 12x-15y=39 \\ \underline{\underline{-+-}} \\ 3x+3y=30 \\ \therefore 3\left(x+y\right)=30 \\ \Rightarrow \left(x+y\right)=10 \\ \therefore \left(x+y\right)=10,\left(x-y\right)=4 \end{gathered}$$