Question

Solve for x and y:
$$\begin{gathered} 23x-29y=98 \\ 29x-23y=110 \end{gathered}$$

Answer 1

The given equations are
$$\begin{gathered} 23x-29y=98.....\left(i\right) \\ 29x-23y=110.....\left(ii\right) \end{gathered}$$
Adding (i) and (ii), we get
$$\begin{gathered} 52x-52y=208 \\ \Rightarrow x-y=4.....\left(iii\right) \end{gathered}$$
Subtracting (i) from (ii), we get
$$\begin{gathered} 6x+6y=12 \\ \Rightarrow x+y=2.....\left(iv\right) \end{gathered}$$
Now, adding equation (iii) and (iv), we get
$2x=6\Rightarrow x=3$
Substituting x = 3 in (iv), we have
$3+y=2\Rightarrow y=2-3=-1$
Hence, $x=3\mathrm{and}y=-1$.