How can I solve this

Question

A certain translation is defined by the rule (x,y)>>> (x+a+b,y+2a-b). Under this translation P(2,3)>>> P’(6,14). Determine and state the values of a and b. Only algebraic solution will be accepted.

Answer 1

(x,y) = (2,3) and (x+a+b, y+2a-b) = (6,14)

So, 2+a+b = 6 and 3+2a-b = 14

a+b = 4

2a-b = 11

3a = 15

So, a = 5 and b = -1.