Mechanism of a hypothetical reaction, $X_2+Y_2\to 2XY,$  is given below:
i) $X_2\to X+X\left(fast\right)$
ii) $X+Y_2\rightleftarrows XY+Y\left(slow\right)$
iii) $X+Y\to XY\left(fast\right)$
The overall order of the reaction will be

Note : Correct the reactions given in question as 
$X_2\rightleftharpoons X+X \left(fast\right)$
$X+Y_2\to XY+Y \left(slow\right)$

Slow step is the rate determining step.
Rate = k[X] [Y₂]
Equilibrium constant for fast step $K=\frac{{\left[X\right]}^2}{\left[X_2\right]}$
$\left[X\right]=\sqrt{K\left[X_2\right]}$
By substituting [X] in equation (i), we get
Rate $=k\sqrt{K\left[X_2\right]}\left[Y_2\right]=K{\left[X_2\right]}^{1/2}\left[Y_2\right]$
$\therefore$Order of reaction$=\frac{1}{2}+1=\frac{3}{2}=1.5$