Raul's family is buying a house on a an odd-shaped lot. the lengths of three of the sides are given by the expressions shown. the remaining two sides lengths are equal to each other. the perimeter of the lot is given by the expression 13y-5. which expression gives the length of the remaining side?

If the perimeter is 13y-5, then it should be equal to all of these sides added together. So, let’s add all of the sides we already know up:

5y-4 + y + 3y+1 = 9y-3.

Now set this equal to the perimeter we already know:

9y-3 = 13y-5. Subtract 9y from both sides.
-3 = 4y-5. Add 3 to both sides.
4y-2.

Now we have the value of 4y-2. Since we know that the last two sides are completely the same, then we can divide this expression by 2.

Therefore, the remaining side is 2y-1.