2x + 5y = 85       (1)    ("The sum of twice a first number and five times a second number is 85.")
5x -  y = 37       (2)    ("If the second number is subtracted from five times the first number the result is 37.")


Multiply the second equation by 5. Keep equation (1) as is. You will get


 2x + 5y =  85     (1')
25x - 5y = 185     (2')


Add equations (1' and (2').


27x      = 85 + 185 = 270   ====>  x = 270/27 = 10.


Then from  eq(2)  y = 5x - 37 = 5*10 - 37 = 50 - 37 = 13.


Answer.  x= 10,  y= 13.