Question

(iii) 35x − 37y = 68; 35y − 37x + 76 = 0

Answer 1

$$\begin{gathered} 35x-37y=68...\left(\mathrm{i}\right) \\ 35y-37x+76=0 \\ \Rightarrow -37x+35y=-76...\left(\mathrm{ii}\right) \\ \mathrm{Adding}\mathrm{eq}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\text{we get:} \\ 35x-37y=68 \\ \underline{-37x+35y=-76} \\ -2x-2y=-8 \\ \therefore -2\left(x+y\right)=-8 \\ \Rightarrow \left(x+y\right)=4 \\ \mathrm{Subtracting}\mathrm{eq}\left(\mathrm{ii}\right)\mathrm{from}\left(\mathrm{i}\right),\text{we get:} \\ 35x-37y=68 \\ -37x+35y=-76 \\ \underline{+-+} \\ 72x-72y=144 \\ \therefore 72\left(x-y\right)=144 \\ \therefore \left(x-y\right)=2...\left(\mathrm{iii}\right) \\ \&\left(x+y\right)=4...\left(\mathrm{iv}\right) \\ \mathrm{Adding}\mathrm{eq}\left(\mathrm{iii}\right)\mathrm{and}\left(\mathrm{iv}\right),\text{we get:} \\ x+y=4 \\ +\underline{x-y=2} \\ 2x=6 \\ \therefore x=3 \\ \mathrm{Substituting}x=3\mathrm{in}\mathrm{eq}\left(\mathrm{iii}\right),\text{we get:} \\ x-y=2 \\ \Rightarrow 3-y=2 \\ \therefore y=1 \\ \mathrm{Hence},x=3\mathrm{and}y=1\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equations}. \end{gathered}$$