Eliminating extra terms.

Adding both equations we get, 9X + 9Y = 54

9(X + Y) = 54

X + Y = 6

$4x+5y=28$ .........................[1]

$5x+4y=26$ ..........................[2]

adding these two equations we get,

$4x+5y+5x+4y=28+26$

or, $9x+9y=54$

or, $9 \times(x+y)=54$

or, $x+y=\frac{54}{9}$

or, $x+y=6$

$4x + 5y = 28 \\ 5x + 4y = 26 \\ {\text{Adding them we get,}} \\ 9x + 9y = 54 \\ \implies 9( x + y) = 54 \\ \therefore x + y = \color{#D61F06}{\boxed{6}}$

Adding the two equations, we get

$9x+9y=54$

Dividing both sides by $9$ , we get

$x+y=\boxed{6}$