I. x + 2y + 3z = 2
II. x + y - z = 0
III. 2x + 2y - z = 1
What is the value of y in the system above?	Choose the correct answer:	A) - 2	B) - 1	C) 0	D) 1	E) 2

Rationale: 1 . from the given system of equations i can make equation ii . to be x + y = z 2 . now put that in iii . : 2 x + 2 y - ( x + y ) = 1 = 2 x + 2 y - x - y = 1 = x + y = 1 that gives usz = 1 ! 3 . put z = 1 in i . and solve : x + 2 y + 3 = 2 ; calculate minus 3 = x + 2 y = - 1 ; calculate minus x = 2 y = - 1 - x ; 4 . now put 2 y = - 1 - x in iii . and solve : 2 x + ( - 1 - x ) - 1 = 1 = x - 2 = 1 ; calculate plus 2 that gives usx = 3 5 . now solve for y with x = 3 and z = 1 : x + y = 1 = 3 + y = 1 ; calculate minus 3 that gives y = - 2 , and hence answer ( a ) - 2
Answer: A