Algebra: A query, not a rant
Mar. 15th, 2011 11:54 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
averygoodun42So, 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, butso 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?
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)
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
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?
