On page 28, question 8, when I looked at the solutions, the number 1 was plugged in to solve the problem. However, on the beginning of the book the author said to never plug 0 and 1…Anyhow, my question is, if never plugging 1 is suggested, how did you know that plugging 1 in would work in your favor for the question(btw I got it right but I didn’t plug 1 in, I thought of other numbers but it did take me longer to figure out the numbers that’d add up to 11)

 
The danger of plugging in 1 or 0, in general, is that those are the multiplicative and additive identities, respectively. That’s a fancy way of saying that multiplying by 1 or adding 0 doesn’t change anything. There’s also the fact that multiplying by 0 turns everything to 0. When you plug in something that doesn’t change anything, or that changes everything to zero, you’re a little less likely to eliminate all the wrong choices, which means you’ll end up having to plug in something else to finish the job anyway. That’s why I advise to avoid plugging in 1 or 0 as a general guideline. The more practice you get plugging in, the more you’ll start to get comfortable seeing when you can ignore that guideline.

The distinction here is that the question tells you that 2x+3y=11, so you’re not randomly choosing 1 as a number to plug in. You’re choosing it within the constraints of the question, and you’re choosing it as part of an ordered pair that satisfies the equation! In the solution, I choose x=3 and y=1, but actually you could also choose x=1 and y=3, or x=2.5 and y=2, etc.

Does that help?