Can you find the identity of ax + by?

Algebra Level 4

\[ \large { \begin{cases} {3a +4x = 6} \\ { 3b + 4y = 1 } \\ { a^2 + b^2= 1 } \\ {x^2 + y^2 = 1 } \end{cases} } \]

Given that \(a,b,x\) and \(y\) satisfy the system of equations above, find the value of \(ax + by \).