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
My $5 Million Dollar Investment That Makes $550 Per Day
What’s up, you Graham? It’s guys here, so let’s finally talk about one of the most requested topics here in the channel, and that would be a complete breakdown of my five million dollar stock market portfolio. Exactly what I’m invested in and my strategy …
Unwanted Visitors- Deleted Scene | Life Below Zero
What I’m doing is the last people that were here, they’re supposed to bring some of their own tarps, spread them out, use their stuff. Um, but instead they use mine. Common courtesy would dictate cleaning them. That’s what I ask: hey, if you’re going to u…
Homeroom with Sal & David C. Banks - Thursday, September 10
Hi everyone, welcome to our homeroom live stream. Sal here from Khan Academy. Really excited about the conversation we’re about to have with David Banks, who is really one of the leading educators in the country, president of the Eagle Academy Foundation.…
Solving equations and inequalities through substitution example 3
Joey is training for a hot dog eating contest. The person who eats the most hot dogs in 10 minutes is the winner. If r is the number of hot dogs that Joey can eat in a minute and n is the total number of hot dogs he eats in the contest, we can write the f…
Golden age of Islam | World History | Khan Academy
[Instructor] In other videos we talk about the rapid spread of Islam, and one of the interesting things about these early Islamic empires is they preserved much of what they inherited from the Byzantine and the Persian empires. The infrastructure, includi…
2015 AP Biology free response 1 a c
Many species have circadian rhythms that exhibit an approximately 24-hour cycle. Circadian rhythms are controlled by both genetics and environmental conditions, including light. Researchers investigated the effect of light on mouse behavior by using a run…