yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Identifying and verifying a solution to a system | Grade 8 (TX TEKS) | Khan Academy


less than 1m read
·Nov 10, 2024

We're told the system of linear equations below is graphed on the coordinate grid. So we can see the graph of ( y = -2X - 2 ) in blue here, and then ( Y = -\frac{1}{4}x + 5 ) in brown here.

What I want you to first do before I do it with you is see if you can visually think about what the solution is to this system. That is, an ( X ) and ( Y ) pair that satisfy both of these equations. Then I want you to verify that it is indeed the solution.

All right, now when I visually inspect it, it looks like this point right over here is on both lines. If I eyeball it, that looks like the point ( x = -4 ) and ( Y = 6 ), so ((-4, 6)).

But let's verify that that indeed is a point on both of these lines. To do that, let's see what ( Y ) is equal to in each of these when ( X = -4 ).

So in that first one, and maybe I'll do it in that same color just to make it a close color. If I say ( Y = -2 \cdot -4 - 2 ), that's equal to positive ( 8 - 2 ), which is indeed equal to ( 6 ).

So for this blue line, when ( X = -4 ), ( Y ) is indeed equal to ( 6 ). Now let's also do it for this brownish-looking line. There, ( Y = -\frac{1}{4} \cdot -4 + 5 ).

So here we have ( -\frac{1}{4} \cdot -4 ) is ( 1 + 5 ), which is indeed equal to ( 6 ). So that point ((-4, 6)) is indeed on both lines.

More Articles

View All
WALL STREET LOSSES! - The TRUTH Behind GameStop, WallStreetBets & Robinhood | Kevin O'Leary
Everybody had just completely discounted. Thought it didn’t matter, and the Robin Hood investors, “Ah, we don’t care about them; they’re too young, they have no money.” Well, that’s not how it is. I can’t stand the arrogance of sophisticated Wall Street i…
Calculating kinetic energy | Modeling energy | High school physics | Khan Academy
In this video, we’re going to talk about kinetic energy, and we’re also going to think about how to calculate it. So, you can already imagine, based on the word “kinetic,” which is referring to motion, that this is the energy that an object has by virtue …
Is All Fair In Love And War?
Hey, Vsauce. Michael here. Love and war are exactly alike. It is lawful to use tricks and slights to obtain a desired end. But is all fair in love and war? That’s a good question; let’s pencil it in for this episode. Of course, pencil is not permanent. It…
Tomasz Kaye designing effective pro-liberty propaganda.mp4
Uh, so thanks for tuning in, everyone. Um, my name is Thomas K. I’m based in the Netherlands, and last year I made the short animated film George Ought to Help, which you can see here, I believe. Um, in case you didn’t see the film before, you can find it…
how to learn a language and never forget it
What was the word? I swear it’s on the top of my tongue. I studied this language for so long, for years, yet I can’t remember this word. If learning languages is a part of your life, I’m pretty sure that forgetting that language after a certain amount of …
She Explores the Universe with Photos, Ink, and Water | Short Film Showcase
[Music] I’ve always been drawn to stories of exploration: the scope of the vision, the ambition of it, the amount of endurance required, and then, of course, the human history of facing the unknown and pushing into it. So, in 2015, my partner, Jamaican A…