2x-5y = 3
 x-2y = 7

Solve the 2nd equation for x

           x-2y = 7
              x = 7+2y

Substitute (7+2y) for x in the 1st equation:

     2x-5y = 3
2(7+2y)-5y = 3
  14+4y-5y = 3
      14-y = 3
        -y = -11
         y = 11

Substitute (11) for y in

         x = 7+2y
         x = 7+2(11)
         x = 7+22
         x = 29

Solution (x,y) = (29,11)

To check, substitute (11) for x and (29) for y
in BOTH of the original equations:

Substituting in the first one:

      2x-5y = 3
2(29)-5(11) = 3
      58-55 = 3
          3 = 3

That checks.  But we must check the solution in
the other equation to show that it checks in both:

       x-2y = 7
 (29)-2(11) = 7
    29 - 22 = 7
          7 = 7

That checks too.  Therefore we now know that 

(x,y) = (29,11) is the correct solution. 

Edwin