The value of 3x-2y is -4. From the equation 5y=6x=16 and 9x=7y-20 the values of (x,y) is (4,8).
Step-by-step explanation:
         The given equations are,
                  5y=6x+16.......................(1)
                  9x=7y-20......................(2)
                 3x-2y...............................(3)
Step:1
     Modify the equations (1) and (2) in (x+y=constant) format,
                 6x-5y=-16.....................(4)
                 9x-7y=-20....................(5)
Step:2
      Equation (4) is multiplied by 7     ( ∵ 7×Eqn(4))
                 42x-35y=-112..............(6)
Step:3
      Equation (5) is multiplied by 5     (∵ 5×Eqn(5))
                45x-35y=-100.............(7)
Step:4
     Subtracting Equation (6) and (7)
                42x-35y=-112
               45x-35y=-100
     ( - )
      (42x-45x)+(35y-35y)=(100-112)
      (-3x)+(0)=(-12)
      x=4
Step:5
     Substitute X value in Equation (1),
              5y=6x+16...................(1)
      where, x=4,
              5y= (6×4)+16
              5y=40
             y= 8
Step: 6
       Check for solution, substitute x and y values in equation (2).
                 9x=7y-20.......................(2)
                (9×4)=(7×8)-20
               36=36
Step:7
       From given, 3x-2y
       where, X=4 and y=8
               3x-2y = (3×4)-(2×8)
                         = 12-16
              3x-2y = -4
 Result:
       The value for 3x-2y is -4. The values of (x,y) are (4,8).