Final answer:
To find the value of y, substitute the values of RS and ST into the equation RT = RS + ST. Solving for y, we find that y = 8. Substituting y = 8 into the equations RS = 9y + 2 and ST = 5y + 6, we find that RS = 74 and ST = 46.
Step-by-step explanation:
To find the value of y, we can use the given information to set up equations involving RS, ST, and RT. Given that RS = 9y + 2, ST = 5y + 6, and RT = 120, we can substitute the values of RS and ST into the equation RT = RS + ST. Substituting the given expressions for RS and ST, we get 120 = (9y + 2) + (5y + 6). Simplifying this equation, we get 120 = 14y + 8. By subtracting 8 from both sides, we obtain 112 = 14y. Dividing both sides by 14, we find that y = 8.
To find the values of RS and ST, we can substitute the value of y into the equations RS = 9y + 2 and ST = 5y + 6. Substituting y = 8, we get RS = 9(8) + 2 = 74 and ST = 5(8) + 6 = 46.