That's looking really easy

A faster method would be

$2y+3x=2(x+y) + x = 18 + x = 22 \Rightarrow x=4 , y=5$

It is a system of equations: $2y+3x=22\rightarrow (1)$ $x+y=9\rightarrow (2)$ Substituting $x=9-y$ into the first equation,we get; $2y+3(9-y)=22\rightarrow 2y-3y+27=22\rightarrow -y=22-27=-5\rightarrow y=\boxed{5}$ Substituting $y=5$ into the second equation,we get; $x+5=9\rightarrow x=9-5=\boxed{4}$ So $xy=4\times5=\boxed{\boxed{\boxed{\boxed{\boxed{20}}}}}$

$2y+3x=2(x+y)+x=2(9)+x=22\implies x=4$ , so $y=9-x=5$

$\therefore$ $x\times y=\boxed{20}$

It was given that,

$2y + 3x = 22$ .............(1)

$x + y = 9$ .....................(2)

Now , from equation (2)

$⇒ x + y = 9$

$⇒ x = 9 - y$ ...................(3)

Placing the value of $x$ in equation (1) to find $y$

$⇒ 2y + 3(9 - y) = 22$

$⇒ 2y - y = 22 - 27$

$⇒ y = 5$

Placing the value of $y$ in equation (3) to find $x$

$⇒ x = 9 - 5$

$⇒ x = 4$

Multiplying $x$ and $y$

$= x \times y$

⇒ $4 \times 5 = 20$

2y + 3x = 22 ----------------------------------- I

x + y = 9------------------------------------------II

Equ I - 2 * Equ II

2y + 3x = 22 ------------------------------------III

-2x - 2 y = - 18 ---------------------------------IV

x = 4

y = 9 - 4

= 5

therefore x * y = 4 * 5 = 20