Feedback on systems-of-eqns

[ToolChainGang]

In reference to version 224734d7be7ff0c4a8adb3a206356ea122112f33

Sect. 1.1: " Example(The Euclidean plane)" each axis has 1 arrowhead, should be 2 or none (each). (To be consistent with R1, which has arrow heads on both ends.)

"pair of real numbers, namely, its x - and y -coordinates": 1st comma should be a semicolon.

"Example(3-Space) ": same comment (about arrow heads) as 2D above. Numerous other examples throughout.

"Example(3-Space) ": triple of real numebrs,

"One Equation in Two Variables": ... the slope is − 1, and the x -intercept is 1. While this statement is correct, in the form shown I've always known the "1" as the y-intercept. This is probably just a matter of style, but I would have expected the equation to be "y = -x + 1" and then state the slope is -1 and y-intercept is 1. This is more in keeping with the low level of explanations given. Perhaps change the example so that the x- and y- intercepts are not the same value, to avoid confusion?

"One Equation in Three Variables": This example would work very well using "click and drag" orientation to clearly see the plane defined by the equation.

"One Equation in Three Variables": The term "implicit equation" is used before it is defined, then the equation shown is not in implicit form. :-)

"both equations true at once. In other words, it as a point that lies on both lines": Probably meant "is". "Point lying" is less passive than "point that lies".

"the lines intersect: therefore, this system has": Colon should be semicolon

"(This solution is ( 3,2 ) , as the reader can verify.)": Consider "The" instead of "this", or avoid the parenthetical altogether using a colon, as in: "( 3,2 ) , as the reader can verify."

" if x − 3 y = − 3, then it is cannot also be the case that": "is" is extra.

"for now we give parametric descriptions in the examples of the previous subsection": Consider making "previous subsection" be the link text.

(Next line): Consider making "this example" the link text, numerous other examples where "example" link would be better as "this example" link. Also, equation is not in implicit form.

In the visualization code for "( x , y , z )=( t ,1 − 2 t , t )", the thermometer display in the "controls" box starts at the middle of the range, and not the left end of the range.

"label the points on the line. However, neither line is the same as the number line": Are you talking about 1 line or two? And if two, what is the 2nd line? This entire paragraph is confusing, consider a complete rewrite (the paragraph).

" like the point ( 0,0,1 )": should be "such as the point ( 0,0,1 )"

Overall, the term "implicit" in the phrase "implicit equation" probably does not add anything. Consider complete removal.