Question

If $12x+17y=53\mathrm{and}17x+12y=63$, then find the value of (x + y).

Answer 1

The given pair of equations is
$$\begin{gathered} 12x+17y=53.....\left(i\right) \\ 17x+12y=63.....\left(ii\right) \end{gathered}$$
Adding (i) and (ii), we get
$$\begin{gathered} 29x+29y=116 \\ \Rightarrow x+y=4\left(\mathrm{Dividing}\mathrm{by}4\right) \end{gathered}$$
Hence, the value of x + y is 4.