Show the solution to 5.4.8.
I don't understand how to solve it the second way.
Its like c/25 + 9 = c/10
Sec I'm on my phone
x + y = 661
10x + 12y = 12x + 10y + 378
y = ?
You're not supposed to use two variables
This is the part of the book before they explain systems of equations
okay replace x with (661-y) and use only y
No I understand the problem it's just needlessly wordy and hard for my brain to parse after 4 hrs
honestly tho just use two variables theres no reason to stay on their progression
Maybe I just have reading comprehension issues
no its fair to think the wording of that problem sucks imo
Same with with the last question too.
The wording sucks and you're really solving for 2 variables but then solving them for one variable.
It's actually a super useful exercise. It makes you parse out a complex issue into a problem. The single variable stuff is done because it helps you understand why reduction of systems of equations works later: it's about reducing many variables to relations of one variable.
But do you agree that you're really solving for 2 variables but then reducing them to get one variable?
The wording of the questions could be better.
Nope, you're solving for one variable. It's simpler to solve mathematically using two variables, but that doesn't build mathematical intuition. It was super frustrating when I was learning that shit, and it was frustrating to watch people learn it for a long time. Once I actually had to teach that level of math and took a pedagogy of math class, I understood why it's good to do these things. It breeds the mathematical maturity that you now have so that you can understand how using two variables and reducing to one is useful and why it works. The complex, shitty wording is actually important in that it forces you to conceptualize things that aren't straightforward
Is this similar to taking a really hard integral and converting it into one with an easy solve?
Yeah: things may be written in a confusing and nearly incomprehensible way, but you have to learn to break it down into intelligible chunks
how is n>=6/36 the wrong answer