RS= 6y +2, St =3y +7, and RT=13y -23

6y

To find the values of y, we can equate the given equations and solve for y.

Given:
RS = 6y + 2
ST = 3y + 7
RT = 13y - 23

We will equate RS + ST to RT: (RS + ST = RT)

(6y + 2) + (3y + 7) = 13y - 23

Simplifying the equation:
6y + 2 + 3y + 7 = 13y - 23

Combining like terms:
9y + 9 = 13y - 23

Moving all the y-terms to the left side and the constant terms to the right side:
9y - 13y = -23 - 9

Simplifying the equation further:
-4y = -32

Dividing both sides of the equation by -4 to solve for y:
-4y / -4 = -32 / -4

Simplifying the equation:
y = 8

Therefore, the value of y is 8.

To find the value of y, we can set up an equation using the given information.

Given:
RS = 6y + 2
ST = 3y + 7
RT = 13y - 23

We know that the sum of the lengths of two sides of a triangle is always greater than the length of the third side. Using this information, we can set up the equation:

RS + ST > RT

Substituting the given expressions:
(6y + 2) + (3y + 7) > 13y - 23

Simplifying the equation:
9y + 9 > 13y - 23

Next, we can isolate the variable by moving all terms containing y to one side of the equation:

9 > 13y - 23 - 9y

Combining like terms:
9 > 4y - 23

Now, we can move the constant term to the other side of the equation:

4y - 23 < 9

Adding 23 to both sides:
4y < 32

Finally, we can solve for y by dividing both sides of the equation by 4:

y < 8

Therefore, the value of y is less than 8.

assuming these are distance between points on a line, you know that

RS + ST = RT
So, just solve for y in
6y+2 + 3y+7 = 13y-23
Then proceed from there to answer any (undisclosed) questions.