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 $ax + by$ .