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http://www.cimt.plymouth.ac.uk/projects/mepres/book9/bk9i5/bk9_5i5.html

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enjoy the magnificent simultaneous equations

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enjoy the magnificent simultaneous equations

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https://maths.mq.edu.au/numeracy/web_mums/module3/Worksheet35/module3.pdf

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try do these in an hour

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http://www.themathpage.com/alg/simultaneous-equations.htm

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a test to try

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BBC - GCSE Bitesize Maths - Simultaneous equations - Higher : Test

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Home > Maths > Algebra > Simultaneous equations - Higher

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http://www.allaboutcircuits.com/vol_5/chpt_4/11.html

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 SIMULTANEOUS EQUATIONS WITH A QUADRATIC 

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 SIMULTANEOUS EQUATIONS WITH A QUADRATIC 

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try to write the equations

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Simultaneous equations are a set of equations which have more than one value which has to be found. At GCSE, it is unlikely that you will have more than two equations with 2 values (x and y) which need to be found.

Example:
A man buys 3 fish and 2 chips for £2.80
A woman buys 1 fish and 4 chips for £2.60
How much are the fish and how much are the chips?

There are two methods of solving simultaneous equations. Use the method which you prefer.

Method 1: elimination
First form 2 equations. Let fish be f and chips be c.
We know that:
3f + 2c = 280 (1)
f + 4c = 260 (2)
Doubling (1) gives:
6f + 4c = 560 (3)
(3)-(2) is 5f = 300
\ f = 60
Therefore the price of fish is 60p

Substitute this value into (1):
3(60) + 2c = 280
\ 2c = 100
c = 50
Therefore the price of chips is 50p

Method 2: Substitution
Rearrange one of the original equations to isolate a variable.
Rearranging (2): f = 260 - 4c
Substitute this into the other equation:
3(260 - 4c) + 2c = 280
\ 780 - 12c + 2c = 280
\ 10c = 500
\ c = 50
Substitute this into one of the original equations to get f = 60 .

Harder simultaneous equations:
To solve a pair of equations, one of which contains x², y² or xy, we need to use the method of substitution.

Example:
2xy + y = 10 (1)
x + y = 4 (2)
Take the simpler equation and get y = .... or x = ....
from (2), y = 4 - x (3)
this can be substituted in the first equation. Since y = 4 - x, where there is a y in the first equation, it can be replaced by 4 - x .
sub (3) in (1), 2x(4 - x) + (4 - x) = 10
\ 8x - 2x² + 4 - x - 10 = 0
\ 2x² - 7x + 6 = 0
\ (2x - 3)(x - 2) = 0
\ either 2x - 3 = 0 or x - 2 = 0
therefore x = 1.5 or 2 .

Substitute these x values into one of the original equations.
When x = 1.5, y = 2.5
when x = 2, y = 2

Simultaneous equation can also be solved by graphical methods.

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Simultaneous Equations | How Do we Solve? | GCSE Maths Guide

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Simultaneous equations are a set of equations which have more than one value which has to be found. At GCSE, it is unlikely that you will have more than two equations with 2 values (x and y) which need to be found.

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http://www.bbc.co.uk/education/guides/zg96fg8/revision

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https://www.youtube.com/watch?v=SqrpJG68EXA

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BBC - GCSE Bitesize Maths - Simultaneous equations - Higher : Test

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Home > Maths > Algebra > Simultaneous equations - Higher

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https://www.youtube.com/watch?v=Lwto-lQzmec

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http://www.mathcentre.ac.uk/resources/Engineering%20maths%20first%20aid%20kit/latexsource%20and%20diagrams/2_13.pdf

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http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/simultaneoushirev1.shtml

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https://maths.mq.edu.au/numeracy/web_mums/module3/Worksheet35/module3.pdf

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Can you solve this?

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http://studymaths.co.uk/topics/linearSimultaneousEquations.php

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Solve these simultaneous equations and find the values of x and y.

Equation 1:  2x + y = 7

Equation 2: 3x - y = 8

Add the two equations to eliminate the ys:

2x + y = 7

3x - y = 8

------------

5x = 15

x = 3

Now you can put x = 3 in either of the equations.

Substitute x = 3 into the equation 2x + y = 7:

6 + y = 7

y = 1

So the answers are x = 3 and y = 1

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http://www.mathsrevision.net/gcse-maths-revision/algebra/simultaneous-equations

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A simultaneous equations question generator

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A simultaneous equations question generator

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Generate a worksheet

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A free worksheet generator that provides pairs of equations in the form 3x + y = 10 that can be solved to find x and y (where the two lines cross).

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A guide to simultaneous equations

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Simultaneous Equations - Elimination method Example 1 : ExamSolutions

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0:00 / 19:19•Watch full video