Question

15x $-$ 17y = 28; 15y $-$ 17x + 36 = 0

Answer 1

$$\begin{gathered} 15x-17y=28...\left(\mathrm{i}\right) \\ -17x+15y=-36...\left(\mathrm{ii}\right) \\ \mathrm{Here}\mathrm{we}\mathrm{observe}\mathrm{that}\mathrm{the}\mathrm{coefficients}\mathrm{of}x\mathrm{and}y\mathrm{in}\mathrm{the}\mathrm{first}\mathrm{equation}\mathrm{are}\mathrm{interchanged}\mathrm{in}\mathrm{the}\mathrm{second}\mathrm{equation}. \\ \mathrm{Adding}\mathrm{these}\mathrm{two}\mathrm{equations},\text{we get}: \\ 15x-17y=28 \\ \underline{-17x+15y=-36} \\ -2x-2y=-8 \\ \therefore -2\left(x+y\right)=-8 \\ \therefore x+y=4...\left(\mathrm{iii}\right) \\ \mathrm{Subtracting}\mathrm{eq}\left(\text{ii}\right)\mathrm{from}\left(\text{i}\right),\text{we get}: \\ 15x-17y=28 \\ -17x+15y=-36 \\ \underline{\underline{+-+}} \\ 32x-32y=64...\left(\mathrm{iv}\right) \\ \therefore x-y=2 \\ \mathrm{From}\left(\mathrm{iii}\right)\text{and}\left(\mathrm{iv}\right)\mathrm{we}\text{get}: \\ x+y=4\mathrm{and}x-y=2 \\ \mathrm{Adding}\left(\mathrm{iii}\right)\mathrm{and}\left(\mathrm{iv}\right),\mathrm{we}\mathrm{get}: \\ x+y=4 \\ \underline{x-y=2} \\ 2x=6 \\ \therefore x=3 \\ \mathrm{Substituting}x=3\mathrm{in}\mathrm{eq}\left(\mathrm{iii}\right),\mathrm{we}\mathrm{get}: \\ 3+y=4 \\ \therefore y=1 \\ \mathrm{Hence},x=3,y=1\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equations}. \end{gathered}$$