Solving Linear-Quadratic Systems

In this video I explain what a linear-quadratic system is, show how to determine the number of solutions to the system, and show how to find the solutions (ie. the points of intersection).

[@peterham8202]

I kind of wish you showed the factoring part :/

[@bigbluedaddy831]

dry

[@jahy5368]

me to

[@ryankieley5924]

Me too

[@markjada]

me too

[@randomstuff3413]

Me too

[@bossguy8301]

Thanks you saved me from reading 4 pages of notes on this now i learned it in 5 min thanks

[@markobaban2261]

Perfectly explained. Good job!

[@edwinzhou827]

Wow. Excellent Explanation.

[@XcomGreat]

Your teaching is soo superb.Dont stop posting

[@nathancolavecchia3410]

Huge help. Thank you for making videos like these.

[@caitlinmorlan496]

omg this is amazing ur literally at my pace! most of the ppl are so slow:( thank you so much!

[@Checkmate489]

Well this just saved my grade in an algebra test (hopefully)

[@philip8673]

Very nice video, very helpful.

[@OgViralShorts09]

I am Simply confused on the factoring. Like in 3x^2-10x+7 has 2 ways to be factored how do you know which to use

[@Darragh-s3e]

Amazing help thank you

[@rylanfroemke8589]

How did u factor that? And can you type the equations into the y= on your calculator then graph then trace and find the solutions that way?

[@MrJamesMath]

I'm not sure how your calculator works, but if it has an equation solver, then yes it would solve the equation for you.
As for how I factored, you could use the Guess and Check or Decomposition methods. Guess and Check is a little too much to explain in a comment, so I'll link to a video I made going through the process. ua-cam.com/video/pjSYHfBcq-E/v-deo.html
If you want to factor using Decomposition, you start by taking the product of the leading coefficient and constant. Since the equation is 0 = 2x^2 - 5x - 3, the product of those will be 2*(-3) = -6. We would like to think of two numbers that multiply to give us this value (-6) but also add to give us the middle coefficient (which is -5). The only two numbers that satisfy this are -6 and +1 (since -6*1 = -6 and -6 + 1 = -5). We are going to use these two values to split, or 'decompose' the middle term like so:
0 = 2x^2 - 5x - 3
0 = 2x^2 - 6x + 1x - 3 (The coefficients of the middle terms are the values we just found. We can do this since they add to -5)
From here we should be able to Factor by Grouping, which involves common factoring from the first two terms and the last two terms which should result in a common binomial factor that we should be able to also common factor. That looks like this:
0 = 2x^2 - 6x + 1x - 3
0 = 2x(x - 3) + 1(x - 3) (Notice both terms contain the binomial factor (x - 3). We can common factor this...)
0 = (x - 3)(2x + 1)
And so it is factored.

[@rylanfroemke8589]

Mr. James thanks for taking the time and doing this. This helped me Ace my math test!

[@mrgoatliri6224]

Is the knowing the bit of how many interceptions worth remembering??

[@elijahsulentic9410]

My discriminate came out with one point of intersection but when I plugged my x value into the initial equations I got 2 points of intersection. Help?

[@MikeMike-yc8gg]

3:05 asking how many points of intersections are they going to be ... one ? two ? none? we have to rely on our descreminate in our quadratic equation ( b^2 - 4ac )

[@milhk]

hell yeah! this helped lots, i appreciate it!

[@Lousybro]

awesome vid thank you so much it helped a lot!

[@MikeMike-yc8gg]

2:35

[@kaprizovis34]

You’re a beast

[@worldoftshirtsontiktok]

Dumb question, why does x=‐1/2 and not just -2? Doesn't 1 go into 2 two times? Then you just add the negative sign?

[@manraj6493]

-1/2 is equal to 1 half, just with a negative sign. Therefore; -1/2 = -0.5. 2 goes into -1, -0.5 times. what ur thinking of is -2/1.

[@jsamunch]

U move faster than the flash ;-;

[@ssj4kevin]

Hey bud, if you check the playback settings then you can slow down the video if you find that I'm going too fast. Sorry!

[@bigbluedaddy831]

what

[@star.15-gk]

Thank you

[@amirgamecelona4596]

Thanks

[@oguzhandemren5737]

You can't factor that part

[@GoodVibesFacts]

yes you can two numbers that add to -5 and multiply to -6 are -6 and 1

[@evanlewis5671]

You move wayyyy to fast:(

[@terrence1q909]

bro its a video you can just pause it

[@XcomGreat]

Please a video on how to find solutions region in linear quadratic systems

[@EpicTgames]

you're supposed to do mod 5,3 on the calculator

[@jonathansmith4065]

What happens if the equation can't be factored. For example -x^2+x+6

[@vline5065]

use quadratic equation to solve for the roots

[@imrllykool]

Much easier however time comsuming and rate of mistakes higher

[@gabi2real]

what did he factor out-

[@laylabergman4823]

i fucking love you sir

[@bruhclay6025]

Bruh

[@evspe5396]

After 3:41 the video made no sense at all

[@Lousybro]

just cuz u dont understand it doesnt mean the vid didn't make sense

[@LaynaCaldwell]

My philosophy is assume nothing... this is the reason for why I disliked the video...

[@Hbdjk552]

Oh my layna! You want a medal for that?

[@adamgamez3471]

God I hate this

[@benburch9529]

this video is pretty much useless unless you are lucky enough to match his situation smh