Final answer:
In the equations provided, the y-value is 3 after setting the sum of the segments equal to the full segment length and solving for y.
Step-by-step explanation:
The y-value is 3.Given the equations RS = 6y + 2, ST = 2y + 7, and RT = 13y - 31, we can set RT equal to the sum of RS and ST because RT is the length of the entire segment, and RS with ST are its parts. This results in 13y - 31 = (6y + 2) + (2y + 7). Simplifying the equation gives 13y - 31 = 8y + 9. Solving for y by isolating it on one side, we get 13y - 8y = 9 + 31,
which simplifies to 5y = 40. Dividing both sides by 5 yields the final answer: y = 8.The y-value can be found by setting RS equal to RT and solving for y.6y + 2 = 13y - 31Subtracting 6y and adding 31 to both sides gives:33 = 7yDividing both sides by 7 yields:y = 33/7Hence, the y-value is 33/7 or approximately 4.71.