Algebra: A query, not a rant

[averygoodun42]

So, I went to the library today to pick up some algebra course books that might actually be helpful. So far, the one I'm using is very helpful. It reminds me that I am not stupid, and that yes, algebra is actually fun.

However...

Can you solve this set of equations?

x = 2y
4x + y = 12



My answer is (8/3, 4/3) or, for those rusty in algebraic notations, x = 8/3, y = 4/3

The book's answer is (4,2)

Both check out. (Erm... right, never mind about that. 12/3 =/= 12... duur.)

But using the substitution method, as we were supposed to, I don't see how (4,2) are derived.

4(2y) + y = 12
8y + y = 12
9y = 12
y = 4/3
x = 2(4/3) = 8/3

Or, you could add a step and solve for x:

y = 1/2x
4x + 1/2x = 12
(9/2)x = 12
(2/9)(9/2)x = 12(2/9) <--- needed visuals to do the maths. It's so bedtime...)
x = 24/9 = 8/3

Where the hell do the whole numbers come into play? I mean, I DO see that they work, but so do the fractions! how do you get them?


I'm not overly concerned about this, seeing as I got every other question I tried right and I understand the methodology. I'm just curious if I'm missing some process for this example or if the book'a author/editor chose a(nother) shady example.

Ach well, it's late. I'll probably look at this problem in the morning and it'll be so obvious I'll cringe and delete this post to hide my shame. But in the meantime, can you explain it?

Comments

[droxy.livejournal.com]

You did this right.

y=12/9 or 4/3 (or 1.33 in decimal format)

A whole number means no decimals (according to my education) So the answer is a fraction, or a "whole number/whole number". Idiot educators. Text books are sometimes wrong or confusing.

If you want to get fancy...you can graph this equation.

[averygoodun.livejournal.com]

Cool! I see that in my bedtime stupor I forgot to multiply 8/3 by 4, so of course I didn't get 12 as the solution when checking my work, and I also didn't note that their answer doesn't check out on the second equation. *rolls eyes at self*

No more math after bedtime, methinks. ;-D

Thanks!

[mischievous-t.livejournal.com]

Yeah, I got y = 1.33, too.

*is confused

[averygoodun.livejournal.com]

Math books really shouldn't be allowed to have typos... ;-)

[pigwidgeon37.livejournal.com]

You did it right, and the book is wrong.
Because for every equation with one unknown, there is only one possible solution. This is why 4 and 2 work for the first but not for the second one -- if you take the first one by itself, with 2 unknowns (huh?), then you have an inifinite number of solutions. But only one of them also fulfills the conditions given by the second (if you substitute 4 and 2 in the second one you get 18=12, which is demonstrably wrong -- you'd have to substitute 2 and 4 in order for it to be correct, but that doesn't work in the first one).
So yay!!!! for you :-)

[averygoodun.livejournal.com]

Right. I was so tired (and my arithmatic so lazy) that I didn't even see that their answer to the second equation was 18 = 12.

I'm relieved that I got it right, but I think from now on I should set the timer and quit doing math after 10 pm. ;-D

Thanks!

[shiv5468.livejournal.com]

They're wrong, you're right

[averygoodun.livejournal.com]

Yay! I like being right. (Even when it means showing to the world how bad my math skills get after 10 pm... ;-)

[randomchris.livejournal.com]

Yep, you're right. The second equation should be 4x + y = 18, or possibly 4x - 2y = 12.

[averygoodun.livejournal.com]

Now that makes sense! Thank you! It must have been a typo on their part. Bad book! Bad! :-D

[ashfae.livejournal.com]

*reads all comments*

Oh good, I got the same answers as you and was wondering what was up...stupid book!