Find the equation of the line that passes through the point of intersection of the lines $3x-4y+1=0$ and $5x+y-1=0$ and cuts the same length from both the axes.  

$\bf{Try:} $
Since the line cuts the same length from both the axes, let the equation of the line be $\frac xa +\frac ya=1$.
The given two lines intersect at the point $\left(\frac 3{23},\frac 8{23}\right)$. Putting this point in the above equation we get $a =\frac {11} {23}$. Hence the equation of the line becomes $23x +23y=11$. But it has two given answers $23x +23y=11$ and $23x-23y+5=0$. I'm unable to find how the second equation comes and why.
Please give reason and describe. Thanks in advance.