►This site was originally created for my kids and their cousins, because we did science together. We eventually added more friends and I ended up having science classes for five years. I am no longer adding to the site (since 2014), but will leave it up for others' use. I do post to facebook occasionally if I come across something to share. =)

►Please accept my apology for any broken links or videos that do not work. I am always disappointed when people take down their videos from YouTube. It makes it hard to find just the right replacement. And because the videos were posted years ago, I usually have no recollection of what the video was about.
I kept thinking I would have time after my kids graduated, but life has filled up my free time with new responsibilities. =)

►Please do not email, asking me to post your website link, or to review something to put on my site. Any resources posted on this site are things I had found on my own during my regular searching for material I needed at the time, and liked it well enough to post here. There have never been any affiliates on my site, and as it is no longer active, would not be worthwhile at this point. ;)
Thank you!

Systems of Equations: Inconsistent/Consistent; Independent/Dependent

When graphing systems of equations, you can figure out whether they are consistent or inconsistent.
If they are consistent, you then see whether they are independent or dependent.

(1) The differences

►If the lines are parallel to each other:
•there is no solution (There is no place of intersection - which would have been the solution, therefore no solution.)
•and they are inconsistent (have no points in common)
►If lines intersect:
•they have a solution such as (2, -4) or where ever they intersect, and that is what you write. "(2, -4)"
•they are consistent (have at least one point in common)
•and they are independent (of each other -- they go their own direction)
►If lines land in the same place, on top of one another:
•the solution is along the entire line - any and all points on the line will work as the solution, so you would say "entire line" or "infinite."  There is an infinite number of possible points along the entire line.
•they are consistent (have at least one point in common)
•they are dependent (do not go their own direction)

(2) Using substitution to tell the difference


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