Devin spent a total of $64 dollars for shoes and a hat. the shoes cost $6 more than the hat. how much did the shoes cost? let shoes be represented by x and hats be represented by y.

By hypothesis, the price of the shoes is represented by x, and the price of the hat is represented by y.
"Devin spent a total of $64 dollars for shoes and a hat" can be represented by the equation x + y = 64
"The shoes cost $6 more than the hat" can be represented by the equation x=y+6

We can now create a system:
x + y = 64 (1)
x = y + 6 (2)

Let's use the value of x from equation 2 and replace in equation (1):
x + y = 64
y + 6 + y = 64
2y + 6 = 64
Subtract 6 from each side to have the variables on a side and the numbers on the other:
2y + 6 = 64
2y + 6 - 6 = 64 - 6
2y = 58
Then divide both sides by 2 to have the variable y alone on the first side and its value on the other side:
(2y)/2 = 58/2
y = 29

We found the value of y.

Now let's use the value of y in equation (1), in order to find the value of x:
x = y + 6
x = 29 + 6
x = 35

We found the value of x.

So the price of the shoes is x = $35 and the price of the hat is y = $29.

You can recheck your answer (very important):
x + y = 29 + 35 = 64 (David spent a total of $64 dollars for shoes and a hat)
y + 6 = 29 + 6 = 35 = x (The shoes cost $6 more than the hat)

Hope this Helps! :)