Question

Find the value of x + y and x $-$ y from the examples given below without solving for x and y:

(i) 4x + 3y = 24; 3x + 4y = 25

Answer 1

$$\begin{gathered} 4x+3y=24...\left(\mathrm{i}\right) \\ 3x+4y=25...\left(\mathrm{ii}\right) \\ \mathrm{Here}\mathrm{we}\mathrm{observe}\mathrm{that}\mathrm{the}\mathrm{coefficients}\mathrm{of}x\mathrm{and}y\mathrm{in}\mathrm{the}\mathrm{first}\mathrm{equation}\mathrm{are}\mathrm{interchanged}\mathrm{in}\mathrm{the}\mathrm{second}\mathrm{equation}. \\ \mathrm{Adding}\mathrm{these}\mathrm{two}\mathrm{equations},\text{we get}: \\ 4x+3y=24 \\ \underline{+3x+4y=25} \\ 7x+7y=49 \\ \therefore 7\left(x+y\right)=49 \\ \therefore x+y=7...\left(\mathrm{iii}\right) \\ \mathrm{Subtracting}\mathrm{eq}\text{(ii)}\mathrm{from}\text{(i), we get}: \\ 4x+3y=24 \\ 3x+4y=25 \\ \underline{---} \\ \mathit{}\mathit{}\mathit{}x-y=-1...\left(\mathrm{iv}\right) \\ \mathrm{From}\left(\mathrm{iii}\right)\text{and}\left(\mathrm{iv}\right),\mathrm{we}\text{get}: \\ x+y=7\mathrm{and}x-y=-1 \end{gathered}$$