$x+2y=5$   ...(1)

$7x+3y=13$  ...(2) 

Let's solve these equations using elimination method.
On multiplying the first equation by 7, we get

$7x+14y=35$   ...(3)

On subtracting (2) from (3), we have 

  $7x+14y=35$

$-7x-3y=-13$
_______________

  $11y=22$
 
$\Rightarrow y=2$ 

On subsituting value of y in  $x+2y=5$, we get
$x+2\left(2\right)=5$
$\Rightarrow x=1$ 

$\Rightarrow x=1$ and $y=2$
Hence, the solution of the given equations is (1, 2).