If xy+z=x(y+z). which of the following mus be true?
A) x=0 , z=0
B) x=1 , y=1
C) y=1 , z=0
D) x=1 , y=0
E) x=1 , z=0
A) x=0 , z=0
B) x=1 , y=1
C) y=1 , z=0
D) x=1 , y=0
E) x=1 , z=0
Given the info we should solve for any number here.
xy + z = x(y + z)
xy + z = xy + xz
z = xz
z/z = x
x = 1
We are down to choices B, D, E,
Check B. ==> X = 1, y = 1, z = 3
We will get equation 1*1 + 3 = 1(1 +3) ==> 4 = 4
Check when z = 0. ==> 1*1 + 0 = 1(1 + 0) ==> 1 + 0 = 1+ 0 ==> 1= 1
Works, but we have to check all other choices.
D. x = 1, y = 0, z = 3
1*0 + 3 = 1(0 + 3) ==> 1 +3 = 0 + 3 ==> 4 >3 DOES NOT work.
Check E.
x = 1, z = 0, y =3
1*3 + 0 = 1(3 + 0) ==> 3 + 0 = 3 + 0 ==> 3 = 3 Works.
But, what if y = 0? Then, 1*0 + 0 = 1(0 + 0) ==> 1 + 0 = 0 + 0 ==> 1> 0, DOES NOT work.
The answer must be B, because it works for all numbers, positive and negative.
