Problem: Let a binary operation ∗ on ordered pairs of integers be defined as (a,b)∗(c,d)=(a−c,b+d). Then, if (3,2)∗(0,0) and (x,y)∗(3,2) represent identical pairs, x equals:
Answer Choices:
A. −3
B. 0
C. 2
D. 3
E. 6
Solution:
By definition (3,2)∗(0,0)=(3−0,2−0)=(3,2) and (x,y)∗(3,2)=(x−3,y−2)
∴x−3=3−0 and y−2=2−0.∴x=6 (and y=4 ).