The Maths Prof: Solve Simultaneous Equations (Linear & Quadratic)

Learn how to solve simultaneous equations when one is a linear equation and the other is a quadratic.

[@lisitenzikamusaro914]

She's the best Math teacher!

[@MinhNguyen-hf9cn]

I love your video. It made my life easier when I deal with Quadratic + Simultaneous Equation. My teacher taught it for three whole lesson but I don’t understand how to solve it but after watching your video, I found out that it just simple steps like that. Thank you very much and hope there will be more videos like this.

[@nonsikelelolorrettandebele1108]

THANK YOU PROFFESSOR WELL EXPLAINED AFTER THIS VIDEO MY MATH STRESS DETERIORATED

[@jeanmutale2710]

Great explaing. Love it when you teach ..you are the best.

[@stanslausmakokha4654]

I'm very grateful for your support in this lesson ❤️

[@courtneyannwatson5153]

Total life saver

[@ahmedshariifsomali8569]

Thank you prof.🎉

[@mohamedmahmoud6753]

You know i didnt understand simultaneous for 2 years and i failed most exams because of it but yourvideo made me understand wighin 10 mins i am fore be er gratefull cuz i have an exam in 2 hours god blessbyour loveely soul

[@abdulwahid3222]

Good explaining

[@itsjomanaaa]

thank you, this was really helpful

[@user-fu6hy2wp2z]

Thank you so much i love you teaching

[@glocku373]

1:40 for those who are confused with how we got -14x ⁉️ I got confused at first too by doing -7 squared but that’s wrong To solve (x-7)^2 you should do the FOIL technique then you’ll get the answer she got

[@rm10gaming73]

Thank you miss you deserve a sub

[@JJTHINGZ]

you are the best many thanks prof

[@frankwewers5819]

Yor, Mam. Best and easy explanation. Thank you

[@twiseels1640]

Really helped thanks

[@jeannkale5721]

Thanks so much

[@dripzabalance]

Great explanation 💯🔥

[@Hujaifa_224]

It was very helpful 👍👍👌👌 The way you teach, makes my understanding easier

[@jeannkale5721]

True

[@t.kuchez14]

you're soo good..please don't stop making videos for us:)

[@virgobeats5586]

From where did you get the 14 from?

[@grassytramtracks]

She expanded the bracket of (x-7)². Do not fall into the trap if writing x²+49, that's not correct. If it helps, write it as separate brackets as (x-7)(x-7): you can then expand them with FOIL to go x²-7x-7x+49 (be careful: timesing 2 negative numbers gives you a positive answer) and you can clean up the middle and that gives you x²-14x+49

[@thegreatjr]

​@@grassytramtrackshuh?

[@user-fn9yt1wv2c]

You are the best🎉❤

[@otlhomamekalayakgosi2351]

Thanks Prof❤

[@Staceygadenya]

thank you so much

[@adesolasalau9188]

Very useful thanks

[@zeemish]

thank you

[@patrickchege3220]

Good teaching 🙏

[@SiphiweThelma-me1zp]

I love your videos can you please do circle geometry

[@aaronalex9474]

Well understood

[@marnedutoit]

Hey, I really like your videos. Is there maybe a chance that you can help me with this linear and quadratic simultaneous equation. X - 5y = -13 and x(squared) + y (squared) = 13. Thank you

[@tejblue2013]

Do u do tuition for o level maths

[@bettyromon8446]

Where is the 49 coming from?

[@awash.6079]

Is it weird that I’m doing this in gcse? Lol but thank you so much, you answered every question i had! You’re made to teach students maths!

[@Joen133]

Okay listen i need an answer for this today!!’ Why did she divide the whole thing by 2??? I never heard of this method before. Is it alternative to something else??? Please answer today🙏🏽

[@hannahventers]

@@Joen133 I know its not the same day, but if it is still useful, dividing the whole thing by 2 just makes it easier to solve the quadratic, and because the equation is equal to 0, you can multiply or divide by anything as 0 multiplied or divided by anything is still 0 😃

[@europa258]

Miss can you please do a video about Ratio problems

[@mahfuzahmed1688]

mam your doing a great job

[@goodnessnmesoma5845]

Pls go through logarithms

[@goodnessnmesoma5845]

Interesting

[@shalifamotaung9110]

what if the are not even number only so do you still divide by 2

[@grassytramtracks]

If there's a common factor you can divide everything. It's optional, if you don't you'll still get the right answer, but dividing everything just makes factorising a bit easier

[@Deekashona5]

Were do you get 14

[@grassytramtracks]

It comes from expanding the (x-7)² which is really (x-7)(x-7) don't fall into the trap of writing x²+49; you have to expand it properly. If you expand out the terms you get x²-7x-7x+49 and you can simplify it to get x²-14x+49

[@user-ne7io5kq5o]

Wow thanks so much but where did you get that 14

[@clergyman3856]

exactly the comment i was looking for, i was beginning to feel like a dyslexic

[@glocku373]

Same here I thought it was gonna be -49

[@glocku373]

Never mind we are wrong 😂

[@grassytramtracks]

I'll try to clear it up: the bracket is (x-7)² and it's an easy mistake to then go x²-49 or x²+49 but you need to expand it with FOIL like usual: you can rewrite it as (x-7)(x-7) if that helps you: and then expand like normal by doing each term in the first bracket and each in the second: that'll give you x²-7x-7x+49 (the 49 is positive because squaring a negative number gives you a positive answer because multiplying 2 negative numbers gives you a positive answer). You can then clean up x²-7x-7x+49 to give you x²-14x+49

[@giftmulonda7114]

I have a question how can you solve this simutanias equestion y+2x=4 and y=x*2+x-3

[@TheMathsProf]

If your second equation is x²+x-3 then it would be like this… Rearrange the first equation to make y the subject y=4-2x. Then you can put the equations equal to each other. Since y equals y, 4-2x=x²+x-3. Then, x²+3x-7=0. You can use the quadratic formula from here to solve and find x

[@sohnafaye]

I love how you explained

[@Joen133]

Why did u divide by 2??? Is that method alternative to somehting else????

[@grassytramtracks]

Everything divided nicely by 2, so you can divide everything through like that if it makes the numbers easier. You don't have to, you'll still get the right answer if you don't, but it just makes it easier to factorise

[@imtiazbinsiraj4920]

How to did you get 14 x?

[@grassytramtracks]

You have to be careful when you square brackets: (x-7)² is not x²-49 because you're really doing (x-7)(x-7) which you have to expand out properly with foil and it gives you x²-14x+49

[@swift-za8390]

thx lad

[@courage6041]

Oct/nov IGs gang??

[@suettaustin524]

I understand up to the point where 7 to the power of two becomes 14 but not how the x comes about making it 14x?????

[@clergyman3856]

exactly, me too

[@clergyman3856]

exactly, me too

[@grassytramtracks]

The (x-7)² is just a shorter way to write (x-7)(x-7) and you then expand that with FOIL like normal: that gives you x²-7x-7x+49 which simplifies down to x²-14x+49

[@Sulaimaneafc24]

How did you get 14x

[@grassytramtracks]

When you expand (x-7)² you're actually doing (x-7)(x-7) which expanded with foil is x²-7x-7x+49 and you can combine the middle terms and get x²-14x+49: that's why it's not just x²+49

[@joegreeves6744]

Can you help me solve 2x+y=5, x^2-y^2=3

[@grassytramtracks]

You can make y the subject of the first one by doing -2x to each side and you get y=5-2x Substitute into the 2nd equation: x²+(5-2x)²=3 Expand the brackets x²+(5-2x)(5-2x) x²+25-10x-10x+4x² x²+4x²-20x+25 5x²-20x+25=3 5x²-20x+22=0 this one doesn't factorise nicely so you have to use the quadratic formula or complete the square (which I'm going to do) Factorise out 5: 5(x²-4x+4.4) Halve the number before the x, put that in the brackets, square what you get after that, and add the number at the end: 5[(x-2)²+4-4.4] 5[(x-2)²-0.4] 5(x-2)²-2=0 5(x-2)²=2 (x-2)²=2/5 square root each side x-2=±√2/√5 Rationalise the denominator x-2=±√10/5 x=2±√10/5 That was a pretty horrid answer and you could put it back into the original equation to find y in each case

[@alyaziaalhammadi7443]

Why is there a 14x?

[@cityentirely5168]

Because -7x-7x=-14x

[@user-qo3vt7eh3f]

Miss I don't understand where you got -14x. Pls can you explain.

[@grassytramtracks]

It's because (x-7)² is NOT x²-49 (try with x as a number, it will not work) you need to expand properly as (x-7)(x-7) where you use FOIL or however you expand brackets and then you get x²-14x+49

[@JoshuaWhitie]

Yes daddy

[@noobmaster1368]

Where did that 14x come from ?

[@ashasingh191]

That's (a+b)²= a²+2ab+b²

[@ashasingh191]

14x is 2ab part

[@shalifamotaung9110]

@@ashasingh191 then how did we get 49 ...I just need explanation with that process please help🥺🥺

[@grassytramtracks]

​@@shalifamotaung9110 what happened was that there was (x-7)² but you can write that out as (x-7)(x-7) and then expand it with FOIL to get x²-7x-7x+49 (the 49 is positive because you're multiplying 2 negative numbers and that gives you a positive answer). That simplifies down to x²-14x+49

[@soundofmillenium01]

i don't understand where you got the 14x

[@grassytramtracks]

When you expand (x-7)², you're really doing (x-7)(x-7) and if you expand that like normal, you get x²-7x-7x+49 which you can simply to get x²-14x+49, that's why it's not just x²+49, which is a very common, and understandable, mistake

[@OlumideMary-cg1mt]

Thank you so much​@@grassytramtracks

[@Aslamido]

😮😮😮

[@Christyyybae]

why is there a 49 in first one

[@courage6041]

-7 squared

[@patrickchege3220]

Just do 7 squared to get 49 it's 7×7 easy

[@grassytramtracks]

That's what -7 squared is because it's -7×-7 and timesing 2 negative numbers gives you a positive number. If you're using a calculator, be careful: always type in (-7)² if you need to square a negative number. If you just type in -7² it interprets it as -(7×7) and will say -49

[@ChristianaOko-hr2wu]

7×7

[@thegreatjr]

If we get 49 where is the 14 coming from 😩

[@obedan3990]

That expansion am confused🤦‍♀️

[@grassytramtracks]

So when it's a whole bracket squared it's the same as (x-7)(x-7), which you can expand out in the usual way but be careful: it's not x²+49. When you expand you get x²-7x-7x+49 and you can then simplify the middle down to -14x

[@starzygh6464]

Please don't understand how you got the 49

[@jonathaniipinge8796]

7x7

[@kirstenfleming3485]

Multiply the minus sevens gives you a positive 49

[@minvs]

STELLAR EXPLANATION!

[@youssefzareli]

Ben

[@ritaella9767]

You didn't break it properly she got me confused