Final answer:
By setting up equations based on the properties of a parallelogram where opposite sides are equal, we find that both x and y equal 5.
Step-by-step explanation:
The problem involves finding the values of x and y for a parallelogram where PT = 2x - 1, QT = x + 4, RT = y - 1, and ST = 3y - 11. In a parallelogram, opposite sides are equal in length, which gives us two equations:
- PT = QT → 2x - 1 = x + 4
- RT = ST → y - 1 = 3y - 11
Now, we solve the first equation for x:
2x - x = 4 + 1 → x = 5
Next, we solve the second equation for y:
y - 3y = -11 + 1 → -2y = -10 → y = 5
Therefore, the values of x and y are both 5.