Answer
The required value is $x=\frac{7}{25},y=-\frac{1}{25}$
Work Step by Step
We know that the system can be rewritten as:
$\begin{align}
& 3x-4y=1 \\
& 4x+3y=1
\end{align}$
And multiply the first equation by 3 and the second equation by $4$ and add them:
$\begin{align}
& 3\left( 3x-4y \right)+4\left( 4x+3y \right)=3\left( 1 \right)+4\left( 1 \right) \\
& 9x-12y+16x-12y=3+4 \\
& 25x=7 \\
& x=\frac{7}{25}
\end{align}$
Substitute the value of $x=\frac{7}{25}$ in the first equation:
$\begin{align}
& 3\left( \frac{7}{25} \right)-4y=1 \\
& \frac{21}{25}-4y=1 \\
& 4y=-\frac{4}{25} \\
& y=-\frac{1}{25}
\end{align}$
