Probably a silly question

[JonDStewart]

using the Kaplan book, the new GMAT Premier Live Online one, and I have this question

30. What is the value of 2x-y

a) x + y = 12

b) X-y = 4


now the way I did it was,

to use (a) x + y = 12
x = 12 -y
plug that into 2x-y to get
2(12-y) -y = 0
24-2y-y = 0
24-3y = 0
-3y= -24
y = 8
plug 8 into x + y = 12 to get x = 4, add those both back into original 'what is the value of 2x-y' to get an answer.

(b) same process

Now the book says that there is no way to get a unique value using this process and that you have to use both A and B to get unique values (I know how to do this, I just thought I could do it quicker the way I did it). So I guess my question is, am I not allowed to do what I did?

When I subtracted 24 from both sides, even though I don't know if other side is zero. Can I not just use zero on the other side? Question is what is 2x-y and I took it as kind of a 2x-y=0 to add the 24...

Like I said, kind of a silly question as I'm guessing I'm just not allowed to do that.

Thanks!

[viju9162]

how did u consider 2x-y =0 ? You cant do that ...

[KapTeacherEli]

Indeed, I'm a little puzzled as to what made you set 2(12-y)-y = 0.

If we substitute as you plan, we get "what is the value of 2(12-y)-y, or "what is the value of 24-3y" We're no closer to solving this than we were before.

[viju9162]

Right Eli. The answer should be "C" right?

[KapTeacherEli]

Bingo, it's C.

If either of the statement simplified to 2x-y, that would be sufficient. Failing that, we need to solve for each of the two variables presented--which means we require to equations.