need help once again

[Guest]

If xy+z=x(y+z), which must be true?

a) x=0 and z=0

b) x=1 and y=1

c) x=1 and z=0

d) x=1 or y=0

e) x=1 or z=0

I did substitute values for the letters x, y, and z on the formula (Ex: using the info. on choice "a" and giving y a value of "2", I substituted like this: 0(2)+0=0(2+0)=0=0), but the weird thing is that all of the answer choices worked out well as the answer to the question. What should I do? :shock:

 

[stapel]

Why substitute? Why not just multiply out the right-hand side, and see what you get?

Eliz.

 

[Guest]

I still come up with two possible answers to this problem: b and c

 

[Denis]

If xy+z=x(y+z), which must be true?
a) x=0 and z=0
b) x=1 and y=1
c) x=1 and z=0
d) x=1 or y=0
e) x=1 or z=0

xy + z = xy + xz
z = xz

choices b) and d) are eliminated, since there's really no y in equation.

a) fits ok, but is not a MUST; same thing with c)

e) is clearly the MUST; one of the 2 choices HAS to be true.

z = xz : divide both sides by z; you end up with x = 1, right?

 

[stapel]

I still come up with two possible answers...

How? Please show your work.

Thank you.

Eliz.

 

[Guest]

thanks!

Thank you Denis! your explanation is perfect!