## How to solve simultaneous linear equations.. using algebra…

These videos show how to solve simultaneous linear equations in steps.

- The first video should be relatively straightforward as it only deals with positive numbers.
- The second is a little trickier (around level B) and involves dealing with a negative term.
- The third video … shows more of a real application..

#### Click here for simultaneous linear equations quick test

Learning how to solve simultaneous linear equations can be important for applications in economics, such as working out the best price to sell a product. This is usually called ‘supply and demand.’

Imagine you make pencils:

- If you sell at a high price they’ll be less demand

- If you sell at a low price they’ll be too many and less profit

Simultaneous equations can be created to show how quantities sold vary with supply and demand. These can then be solved to show the best price to make sure you sell your pencils, and the demand continues.

Another example – a favourite in exams – is to use mobile phone contracts. Sometimes these are given as a graph and there’s more about this in the next post. Although the question is usually two linear equations, and it asks you to pick the best value.

One of my favourite exam questions involves The Khans and The Smiths buying theatre tickets. Each family has got different numbers of adults and children … and you need to create a couple of simultaneous equations to work out the price of each ticket.

These kind of questions may be a little strange (why didn’t they just ring the box office?), but they do give an insight into how equations work. There are other examples such as arranging a meeting half way through a journey or working out the cost of bank loans.

Please add a comment below with any more real life examples.

Watch the videos on YouTube:

How to solve simultaneous linear equations using algebra

How to solve simultaneous linear equations using algebra

How to solve simultaneous equation word problems

Georgie says

r+s/8s = r-s/8n

I have this equation to rearrange to make r the subject (apologies, but don’t have a divide button on my computer!!!!!!)

I’m really confused so would appreciate any feedback you have that could help me

Many thanks

Simon says

Hi Georgie

I’ve been working through this but please could you check the question? The couple of solutions I have cancel out the r (as it’s just one value of r each side).

Renea Chua says

How do you do this:

a – 5b = -12

8a + 3b = -10

MagicMinter HD says

wtf i did the same method with this question and didnt get it right

4x+y=25

x-3y=16

InsaneGamer says

where have you been all this time??

SuperSonicSpeedGuy says

The camera keeps going all blurry, like at 4:00 🙁 But thanks for the vid!

Hannah Dale says

Thank you so much for these videos! I’m currently revising for end of year

exams and this is helping alot! Very much appreciated.

sandev randhawa says

great video to watch

Ajit King says

did you know science

Ajit King says

you are a very good teacher dude.

CoolCat4196 says

I have this equation that I would like you to help me with, if possible.

Parking Station A: charges $3.20 (first hour) and $2.00 (afterwards)

Parking Station B: charges $6.00 (first hour) and $1.20 (afterwards)

Calculate the times of parking which would result in the cost being the

same at both parking stations.

I hope that you can help, Thanks and you are great

kurtis sankey says

having trouble with this one A television repair person charges a service

call of $36 and then a further $28 per hour. An electrician charges a

service call of $24 and then a further $36 per hour. Use simultaneous

equations to calculate the number of hours each person worked to charge the

same total fee. What is the fee?

Ahmed El-Aide says

there is a question I found and I couldn’t solve it please help me

the cost oh hire a tent consists of two parts

$C and $D per day ( there is a plus sign in the place of “and”)

total cost for 4 days is $27.1 and for 7 days $34.30

write down the 2 equations

J. Moore says

THANK YOU SO MUCH YOU HAVE SAVED MY LIFE

unknown profile says

a and b are positive whole numbers.

find value of a and b to make the solution to this equation x=4

a(x+1)+b(x-2)=16 please help me if you can 🙂

Lee Dodd says

Do you have any videos on Algebra and area.I am not sure what the correct

name for it is, EG A triangle is drawn with 3x-15 then 2x-24 then one side

saying x+2.Then you have to work out the Perimeter.

The Astute Atheist. says

Hey, it may be a bit late, as the video was uploaded two years ago

(almost). But I have a question, and I have NO clue how to do it. It’s a

big one with a table so I will try my best:

*Question:*

A company makes three types of patio furniture, chairs, rockers and chaise

lounges. Each require wood, plastic and aluminium, as given by the table

below. The company has 400 units of wood, 600 units of plastic and 1500

units of aluminium.

*Table:*

Wood Plastic Aluminium

Chair 1 Unit 1 Unit 2 Units

Rocker 1 Unit 1 Unit 3 Units

Chaise Lounge 1 Unit 2 Units 5 Units

For it’s end of season production run, the company wants to use up ALL the

stock. To do this, *calculate* how many chairs, rockers and chaise lounges

should the company make?

*We have been doing simultaneous equations and linear functions in class,

that could help*. I really need help so, it’d be REALLY awesome if you

could help me out.

ABDUL JAWAD Ghalib says

I hav given a symultaneous equation word problem it would be a grateful if

you kindly give the solution of the following question:

At a shooting range, each shot costs 20c. If you hit the target, you

receive 30c. Mira has 20 shots and makes a loss of 70c. How many hits did

she get?

On The Road Media says

“Solve algebraically these simultaneous equations.”

y= 4x² – 9x -1

y= 5-4x

willoxens says

Could you help me with a question?

It asks to consider the equations:

(k-3)x+5y=-2

2x-3y=4

where k is a real constant for which I have to find the unique solution.

Thanks in advance!

Ambra Onyss says

where did x=4 come from?

yassin ramadan says

thanx a lot you really did help with this. im going to do my GCSE after a

month so thanx again

hi ih says

how is it x=4? where did this come from? it got me so confused. pls reply

CoD Shotz says

Thank you this was really helpful.

stephen barker says

q1 there are 1130 pupils in a school and no classes have more than 32

pupils. how many classrooms could be used show this information as an

inequality. q2 a person is prepared to spend £300 taking friends

out to celebrate. if the restaurant charges £12 per head how many guests

can be invited show this information as an inequality can you help please

Shoot Fresh Mine says

hey can u help me answer these questions

-5m-3n=-3

10m-7n=-12

AND

-2v+w=-19

-2v-7=21

thanks

Shoot Fresh Mine says

Hey I got a question which I need help with working out.

3u+v=17

7u+v=29

Dafydd Morris says

How would I do

4x+3Y=12

6x+2Y=13

Dafydd Morris says

Praise be Simon deacon 😀

Shoot Fresh Mine says

How would u work out

3p+5q=43

8p+5q=73

Cethical says

You’re such a humble bloke. I miss London just because of your manners.

ABWEndon says

Thank you Simon. Very well explained and although my brain hurts a little,

I can feel that it has done me some good!

vani na says

thank you so much

Phase Gaming says

thanks i have a maths test coming up and you relay helped

stephen barker says

have i got this right if both equations are + you subtract if both

minus you add and 1 of each you add

Mathew Stenton says

Wow Simon your my best friend and I love you thanks

OpiumMessiah says

Thanks, man. 🙂

Phoenix Feathers says

Thank You, Thank You, Thank You!!!!!!

Charlie Michele says

Thank you so much! I finally get it!

Daniel Gadd says

2y = 5x + 7

3y = -2x -5

Help me here someone please

Daniel Kibby says

I’ve watched 3 of your videos as I am retaking my Maths GCSE and found them

very helpful. Thank you.

Walter Payton says

it helped me ooooooooooooooooooooooooooooooooooo!!!! may god bless you sir

MegaSaya64 says

thankkk

Hayden Nicholson says

Thanks +Simon Deacon helped alot!

bubbles xo says

very helpful cheers

Marcin Szostok says

THANK YOU !

thejchan16 says

Thanks for the video! It was so helpful leading up to my Maths Test. You

are such a great teacher! Keep doing what you do because your awesome!

Michelle Wanha says

Thank you sir!

Mateen Malik says

Thanks makes a lot more sense.

Jose Dominguez says

Fix the audio

ibraheem nawaz says

Awesome Best tutor you are better than my maths teacher.. 🙂

Tendaishe Mbele says

thank you so much, i was confused before i watched this video 😀

stephen barker says

im trying understand something quadratic equations no 1 x sqaured

minus x minus 56 =0 changed from minus b at start to positive minus minus

is a plus comes out right as 8 and minus 7 next question 3x sqaured +

7x minus 13 =0 but with this one if you change the minus at start to plus

answers in back of book are different to what it comes up with any advice.

Matthew Sydoruk says

hi

stephen barker says

can you check some equations been told there wrong 4x plus 2y = 12 x +

2y = 6 2y cancels out 4x minus x = 3x 3x = 12 minus 6 is 6 so x = 2 2

plus 2y = 6 y = 2 so x is 2 and y is 2 been told can only use each

number once

yukicross6767 says

you see i have this equation tht i dont get may u help me?

see i have {5x+2y=19 … 1

{2x+3y=12 …2

but i dont get how you r suppose to multiple this by 3 for the top and then

u need to multiple by 2 for the second part

Peter Backstrand says

how became x=4 all of a sudden? 7:45

stephen barker says

how do you solve simultanious equations graphically

Jibrael Malik says

Thanks helped me out!

stephen barker says

i do simultanious equations using the same method as in the vid

HilalFener says

Why is y=2? im kind of confused how you got 2

stephen barker says

got it. if a farmer wishes to promote the white ridge back sow as the most

prolific breeder then which of the 3averages would he not include

stephen barker says

youll have do some with minus terms

stephen barker says

how would i solve x squared + y squared = 29

and y _ x = 3

Josh Shil says

Hi Simon Deacon I am looking for questions that give the answer of both x’s

and both y’s FOR SOLVING SIMULTANEOUS LINEAR EQUATIONS. Thank you

stephen barker says

x squared +y squared = 29 y minus x = 3 thats the first set set 2 is y+ 1

=x squared and x = y minus 1

Cameron Richmond says

Very useful doing this in maths and I didn’t understand it till now and I

can solve these in my up and coming maths exam

davidymcmb says

Thanks for the help man!

stephen barker says

ive nailed equations with minus numbers already for next year now

BAT TT says

This is very helpful thank you

Justin Beary says

Thank you so much I finally understand how to do it without making stupid

mistakes wuhuuuuu!

Annie Lim says

it is really blur

mussa sherif says

Thanx

killa killa says

Thanks you really helped I have a test tomorrow-hope I do well

stephen barker says

i make 1 letter the same in both equations subtracted answers gets

remaining letter

mohamed abdelhalim says

thanks !!! really did help.could you solve this question for me please. A

submarine can travel at 25 knots with the current and at 16 knots against

it .Find the speed of the wind and the speed of the submarine in still

water.

SkizaKiza says

thankyou for the help!

Simon Deacon says

Please like and leave a comment!

Visit https://www.3minutemaths.co.uk for real maths, tips and techniques.

Satellite Dave says

Thank you very much!! Your video helped me a lot!

Finlay McKee says

I have my GCSE’s this year and you have managed to teach me what my maths

teacher has failed to. Thank you so much!

Anita Cheung says

thanks

Simon Deacon says

Hi – you need to plot both lines and see where they cross. It’s OK if you

have an idea where they are likely to be on a graph… but it can take a

long time to get that information. I’ll post a video on this and let you

know. Simultaneous solving by using algebra is better and easier. All best S

stephen barker says

a graph how would i do that

Simon Deacon says

Hi – this is really the easiest way. You could solve by plotting a graph

but it takes a while and isn’t always very accurate. Keep practicing and

good luck!

stephen barker says

whats the easyest way to solve these

Simon Deacon says

Hi – Q2 needs a bit more explanation. If you email me through Maths Wrap I’ll send a solution. In the meantime Q1:

You’ve got 2 equations J = 2L and J + L = 5L – 48.

So, change both and you’ll get J-2L = 0 and J-4L = -48. Then take eq2 from eq1 and you should get -2L = -48. So L = 24.

Put L=24 back into eq1 and J = 48.

So Jan is 48 and Lisa is 24.

I hope this helps and all best S

mymindydiditong says

*two

mymindydiditong says

Hi, im not sure how to solve these teo problems:

1)Jan is twice as old as Lisa. The sum of their ages is 5 times Lisa’s age minus 48. How old are they now?

2)John received changes worth $13 all in coins. He received 10 more dimes than nickles, and 22 more quarters than dimes. How many coins of each did he receive?

Simon Deacon says

Hi Mustanser – glad you liked the video and thanks for the comment 🙂

The first equation is F = 3S . The second is a little more difficult. Imagine 10 years ago … at that stage the father would be F – 10 and the son would be S – 10.

However the dad is 5 times older so F – 10 = 5 (S – 10). Now you’ve got two equations F = 3S (or F – 3S = 0) and F – 10 = 5S – 50 (or F – 5S = -40). Take equation 2. away from equation 1. You should end up with the son aged 20 and the dad aged 60. All best S

mustanser hussain says

ago*

mustanser hussain says

Hey,this was very useful indeed,thankyou.Can u give me the solution for this problem. A man is 3 times the age of his son.10 years aga he was five times the age of his son.Find their ages by finding the value of x.

Simon Deacon says

Hi Glen – when I posted this it took out the new lines and doesn’t look as neat. I hope you can follow. If not please send your email address through mathswrap and I’ll send a reply.

Simon Deacon says

Hi Glen – you’ve got two equations:

C + Z = 25

3.2C + 1.4Z = 62

Multiply first by 3.2 (and leave second) so:

3.2C + 3.2Z = 80

3.2C + 1.4Z = 62

Take second from first, so:

1.8Z = 18

Therefore Z = 10

Then put back into

C+ Z = 25

C + 10 = 25

So C = 15

The alloy has 15kg of copper and 10kg of zinc.

I hope this helps and thanks for the question.

All best

S

Simon Deacon says

Hi Glen – you’ve got two equations:

C + Z = 25

3.2C + 1.4Z = 62

Multiply first by 3.2 (and leave second) so:

3.2C + 3.2Z = 80

3.2C + 1.4Z = 62

Take second from first, so:

1.8Z = 18

Therefore Z = 10

Then put back into

C+ Z = 25

C + 10 = 25

So C = 15

The alloy has 15kg of copper and 10kg of zinc.

I hope this helps and thanks for the question.

All best

S

Glen Rossow says

The materials to make 25kg of an alloy of copper and zinc cost $62. If the copper costs $3.20/kg and the zinc costs $1.40/kg, find the composition of the alloy.

How would i do that problem?

Kim Khus says

it helps me thanks

Simon Deacon says

Hi – generally yes, although you might need to change the equations a little. Thanks for the comment 🙂

zareensaba says

So Mr Simon .if we have two turms negative equation we add after we multiply .and with positive equations we subtract after the multiplication.right?!

Devansh Sangoi says

oregata

Simon Deacon says

Hi Ayisha – no, numbers change, although most examples tend to use ‘easier’ numbers. I’ll post a video with some harder questions and let you know when done. All best S 🙂

ayisha asuni says

anytime you have an equation do u always have to use the numbers 3 and 4

Simon Deacon says

Hi – yep – went out and bought a better camera soon afterwards! Thanks for the comment and hope the vid was helpful 🙂

Ciara Mcsorley says

the only downside is that it isn’t in focus!!

Simon Deacon says

Hi – this would be around B grade. If there was a ‘word’ problem that you needed to create the two equations, it would be an A / B.

Georgia Pennant says

What grade is this?

KellyReveiw says

thanks !!! really did help 🙂

Simon Deacon says

Hi … hmm. There could be a way of getting a -7.5 if the width was also negative in your calculation. For most questions they would expect you to then convert to both positive numbers – and say the pool is 7.5m width. My email is on mathswrap – if you send me a copy (photo is fine) of your working – I’ll mark and email back. Hope this helps. S

Nada Abdalla says

would it still be correct if we wrote that the width is equal to -7.5?

David Taylor says

The step by step approach is just what students need and the inclusion of real life examples (why we learn this in the first place) is a great bonus.

Simon Deacon says

🙂 thanks

lordmoonaz69 says

Cool, thanks for your videos 🙂 you make it so easy to understand

Simon Deacon says

Hi I’m a maths tutor and also run three first class learning centres.

lordmoonaz69 says

Are you a maths teacher?

Simon Deacon says

Simultaneous word problems coming soon!