Final answer:
The value of y is 8. By substituting y into the expressions for RS and ST, we find that RS is 77 and ST is 46.
Step-by-step explanation:
To find the value of y, we use the fact that RS + ST = RT. Given that RS = 9y + 5, ST = 5y + 6, and RT = 123, we can set up the following equation:
9y + 5 + 5y + 6 = 123
Combining like terms, we get:
14y + 11 = 123
Subtracting 11 from both sides gives us:
14y = 112
Dividing both sides by 14 gives us the value of y:
y = 8
Now that we have the value of y, we can find RS and ST.
RS = 9y + 5 = 9(8) + 5 = 72 + 5 = 77
ST = 5y + 6 = 5(8) + 6 = 40 + 6 = 46