Question:
If the ordered pairs (x, −1) and (5, y) belong to the set {(a, b) : b = 2a − 3}, find the values of x and y.
Solution:
The ordered pairs (x, −1) and (5, y) belong to the set {(a, b) : b = 2a − 3}.
Thus, we have:
x = a and −1 = b such that b = 2a − 3.
∴ −1 = 2x − 3
or, 2x = 3 − 1 = 2
or, x = 1
Also,
5 = a and y = b such that b = 2a − 3.
∴ y = 2(5) − 3
or, y = 10 − 3 = 7
Thus, we get:
x = 1 and y = 7