3y = 2x-6
x + y =8
solve algebraically.

    3y = 2x - 6   Solve one equation for a variable. I'll solve the second one for   x + y = 8           y.

x + y = 8         Subtract x from both sides
      y = 8 - x  

Now, substitute this y value (8 - x) into the other given equation and solve for x.

       3y = 2x - 6    Replace y with 8 - x
3(8 - x) = 2x - 6    Multiply 3 (8 - x)
24 - 3x = 2x - 6   Add 3x to both sides
       24 = 5x - 6   Add 6 to both sides
       30 = 5x        Divide both sides by 5
         6 = x           Flip the equation to make it easier to read
         x = 6

Now, use the x + y = 8 equation, replace the x with 6, and solve for y.

x + y = 8             Substitute x for 6
6 + y = 8             Subtract 6 from both sides
      y = 2

Check your answers in both equations.

  3y = 2x - 6      Replace x and y with 6 and 2
3(2) = 2(6) - 6   Simplify 3(2)
    6 = 2(6) - 6   Simplify 2(6)
    6 = 12 - 6      Subtract
    6 = 6

 x + y = 8   Replace x and y with 6 and 2
6 + 2 = 8   Add
      8 = 8

So, the answers to your system of equations are x = 6 and y = 2 .