Let x = the price of the pair of shoes and y = the price of one pair of socks.


Then from the condition you have this system of 2 equations in 2 unknowns.


2x + 4y = 117,      (1)
3x + 5y = 170.      (2)


Solve it by the Elimination method.

For it, multiply eq(1) by 3 (both sides) and multiply eq(2) by 2 (both sides). You will get


6x + 12y = 117*3     (3)
6x + 10y = 170*2     (4)


Now subtract eq(4) from eq(3).  The terms " 6x " will cancel each other, and you will get a single equation for the unknown y only.

          (It is how the Elimination method works.)


   12y - 10y = 117*3 - 170*2

   2y = 11  ====>  y = 11/2 = 5.50 dollars.


Then from eq(1)  2x = 117 - 4*y = 117 - 4*5.50 = 95  ====>  x = 95/2 = 47.50 dollars.


Answer.  $47.50 for the pair of shoes and $5.50 for the pair of socks.