Simaltaneous equations

[Creamlegbar]

So far,

there are 2 methods.

1. balance method
2. substitution method

How do I know which to use?

If I use the balance method, ie, adding or subtracting one equation from another, do I just multiply one of them first to get 'like terms' to cancel out?

And then, there is the graphic method. When do I use that?

Any help gratefully received. I seem to remember finding s.e.s 'fun' when I did them for O levels. I just haven't 're-got it' yet.

I want my ds to find them fun but I need to remember myself first.

The methods are interchangeable. You can use whichever one seems easiest to solve a particular set of simultaneous equations. There are no rules as far as I know. I tended to use what you are calling the balance method (haven't heard it called that before - we called it the elimination method) pretty much all the time unless the question specified that another method was to be used. And yes, you multiply both sides of one equation before adding or subtracting it from the other in order to eliminate one of the variables.

You use whichever method is easier. Elimination (balance) usually works best until Alevel.

I will do you an example.

3x +2y = 18
5x + 3y = 29

You choose whether to make the x or y the same.
I choose x so multiply top one by 5 and bottom one by 3 (multiplier of x in other equation)

15x + 10y = 90
15x + 9y = 87

You now have 15x in both, and they are both positive so you need to take away. If one positive and one negative you add

0x + y = 3

y=3

Now substitute this into either of the equations.
I choose top one

3x + 2(3) = 18
3x + 6 = 18
3x = 12
x = 4

The last thing ALWAYS to do is put both nunbers into other equation to check

5x + 3y = 29
5(4) + 3(3)=
20 + 9 = 29
check

Graphical is usually only for approx answers when exact methods can't be solved.
ie one quadratic at GCSE level.

BBc bitesize has more here

We have two equatioons in the format, say, of 2x= 5y+6. These equations can be drawn on a graph and will produce a straight line. Draw both straight lines and where they intersect gives you the resulting values of x and y.
The algebraic method is superior because it is precise. The graphical method depends on how good your drawing skills are!
link

Thank you everyone.

The book I am using is 'National Curriculum Mathematics 7', by KM Vickers and MJ Tipler.

I used to think that I was good at maths but I am realising (although I always knew this too) that I had VERY good maths teachers, who could basically get a monkey through O level maths.

I will mull over all that you have said and try and do the exercises myself.

When does the graphic method come in?

I BLOODY LOVE MUMSNET, I really do.

Thank you all, I can't believe you replied so soon. So, balance method is the default option for now?

When does the 'graphic' method of solving become relevant?

I am using 'National Curriculum Mathematics (with answers) by KM Vickers and MJ Tipler.

I am realising (although I knew it already) that I had VERY good maths teachers.

I will try and solve them myself with your helpful suggestions. I really want him to find them as easy as I used to but unfortunately maths doesn't seem as easy to re 'get' as biking.

THANK YOU!!!

The graphic method is only really useful for approximate answers. I think the main reason for using it is to help students understand what is going on.

I discovered Khan Academy recently(after hearing about it ages ago!) It has some great free tutorials on "Solving Systems" as the Americans call it. He explains the types of questions where each method is used.
.
Hope this helps!

Thanks Caroline. I have just had a look. I will be back when we get onto Quadratic equations. Thank you all. Clb.