# Modular Equation 1

If $$x , y$$ are integers that satisfies the conditions below,

$\displaystyle \begin {cases} 4x + 5y \equiv 9 \mod 23 \\ 5x + 11y \equiv 9 \mod 23 \\ x , y > 0 , \end {cases}$

What is the value of $$(x+y) \mod 23$$ ?

×