# How to solve simultaneous linear equations … using algebra

## 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

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Filed in: Higher • Maths Videos • Quick reminder maths

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

THANK YOU SO MUCH YOU HAVE SAVED MY LIFE

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

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.

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.

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?

“Solve algebraically these simultaneous equations.”

y= 4x² – 9x -1

y= 5-4x

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!

where did x=4 come from?

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

month so thanx again

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

Thank you this was really helpful.

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

hey can u help me answer these questions

-5m-3n=-3

10m-7n=-12

AND

-2v+w=-19

-2v-7=21

thanks

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

3u+v=17

7u+v=29

How would I do

4x+3Y=12

6x+2Y=13

Praise be Simon deacon 😀

How would u work out

3p+5q=43

8p+5q=73

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

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

I can feel that it has done me some good!

thank you so much

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

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

minus you add and 1 of each you add

Wow Simon your my best friend and I love you thanks

Thanks, man.

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

Thank you so much! I finally get it!

2y = 5x + 7

3y = -2x -5

Help me here someone please

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

very helpful. Thank you.

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

thankkk

Thanks +Simon Deacon helped alot!

very helpful cheers

THANK YOU !

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!

Thank you sir!

Thanks makes a lot more sense.

Fix the audio

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

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

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.

hi

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

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

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

how do you solve simultanious equations graphically

Thanks helped me out!

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

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

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

youll have do some with minus terms

how would i solve x squared + y squared = 29

and y _ x = 3

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

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

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

Thanks for the help man!

ive nailed equations with minus numbers already for next year now

This is very helpful thank you

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

mistakes wuhuuuuu!

it is really blur

Thanx

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

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

remaining letter

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.

thankyou for the help!

Please like and leave a comment!

Visit http://www.mathswrap.co.uk for real maths, tips and techniques.

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

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!

thanks

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

a graph how would i do that

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!

whats the easyest way to solve these

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

*two

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?

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

ago*

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.

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.

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

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

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?

it helps me thanks

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

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?!

oregata

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

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

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

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

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.

What grade is this?

thanks !!! really did help

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

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

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.

thanks

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

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

Are you a maths teacher?

Simultaneous word problems coming soon!