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Simultaneous equations. Yes, I know we’ve done this but you were a little ropey last week. 4 ways of solving them. Pros If you guess well, then easy to solve. Cons Hard to show your working. Only works for really simple ones. Can take a lot of time. 1 Guessing the answers. Pros

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Simultaneous equations

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Simultaneous equations l.jpg

Simultaneous equations

Yes, I know we’ve done this but you were a little ropey last week.


4 ways of solving them l.jpg

4 ways of solving them


1 guessing the answers l.jpg

Pros

If you guess well, then easy to solve.

Cons

Hard to show your working.

Only works for really simple ones.

Can take a lot of time.

1 Guessing the answers.


2 by adding subtracting equations traditional method l.jpg

Pros

Works for all but the most complicated equations( A – level).

Will give exact answer.

Cons

Need to show all working and work carefully.

May need to multiply equations first

2 By adding/subtracting equations(traditional method)


3 graphically l.jpg

Pros

Will work every time

Works for families of equations

Cons

Not always accurate

Time consuming

Long-winded, lots of room for mistakes to creep in.

3 Graphically


4 substitution l.jpg

Pros

Can be quickest way

Best way for complicated equations e.g.. powers

Cons

Not suitable for all equations

More likely you are looking at A – level paper.

4 Substitution


Traditional approach l.jpg

Traditional approach


2x 2y 8 3x y 16 l.jpg

2x + 2y = 83x – y = 16

Number equations

2x + 2y = 8

3x – y = 16

Make ‘y’s the same by multiplying

x 2 6x – 2y = 32

1

2

2

3


2x 2y 8 3x y 169 l.jpg

2x + 2y = 83x – y = 16

2x + 2y = 8 Same no. of y’s in

3x – y = 16

6x – 2y = 32

DIFFERENT signs so ADD

+ 8x = 40

x = 5

1

1

3

2

3

1

3


2x 2y 8 3x y 1610 l.jpg

2x + 2y = 83x – y = 16

2x + 2y = 8

3x – y = 16

Substitute x = 5 in (easiest)

2 x 5 + 2y = 8

10 + 2y = 8

2y = -2

y = -1

1

2

1


Almost there l.jpg

Almost there


2x 2y 8 3x y 1612 l.jpg

2x + 2y = 83x – y = 16

We have x = 5 and y = -1 so now we

CHECK IT

Check inbecause we haven’t used that yet

(3 x 5) – (-1) = 15 - - 1

= 15 + 1

= 16

2


And finally l.jpg

And finally…..

Don’t forget to write your answers down clearly

x = 5 and y = -1


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