Let x be the cost to rent a chair;  

let y be the cost to rent a table.


Write two equations for two unknowns as you read the problem

    3x  + 5y = 57     (1)

    12x + 2y = 39     (2)


This system is good to solve it by Elimination.  For it, multiply equation (1) by 4 (both sides).
Keep equation (2) as is.  Then you have this modified system

    12x + 20y = 4*57      (3)

    12x +  2y =   39      (4)


Now subtract equation (4) from equation (3).  The terms with "x" will delete each other,
and you will get an equation for single unknown "y"

         20y - 2y = 4*57 - 39

Simplify and find y

            18y  = 189

              y  = 189/18 = 10.50  dollars.


Then from equation (2) find 

    12x + 2*10.50 = 39

    12x           = 39 - 21 = 18

     x                      = 18/12 = 1.50 dollars.


ANSWER.  It cost $10.50 to rent one table and $1.50 to rent one chair.


CHECK.   To check, substitute the found values into original equations:

         Eq(1):  3*1.50 + 5*10.50 = 57 dollars,  correct.

         Eq(2): 12*1.50 + 2*10.50 = 39 dollars,  correct.