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Please help me with simultaneous equations
By Laura-Anne Robinson (P1563) on Saturday, December 4, 1999 - 03:43 pm:

I need to know how to work out simultaneous equations i.e.
3p + 4q =2q
5p - 2q = 5
What do p & q equal?
Please use simple english, Many thanks....

By Peter Robinson (Pmpfr2) on Saturday, December 4, 1999 - 04:49 pm:

Hi Laura-Anne

You need to make the problem easier by removing one of your unknowns (say q). Then, you can find p and then you can find q.

Start from your simultaneous equations which I will call (1) and (2):

3p + 4q = 2q ...........(1)
5p - 2q = 5 .............(2)

(1) has two q terms. These can be 'collected together' by subtracting 2q from both sides:

so (1) becomes:

3p + 4q - 2q = 2q - 2q
3p + 2q = 0 ...........(3)

Now, noticing that both (2) and (3) have 2q in them, I will solve (3) for 2q by subtracting 3p from both sides of (3) so that (3) becomes:

3p + 2q - 3p = 0 - 3p
2q = -3p ...............(4)

Now, I can replace the 2q term in (2) using (4)

(2) is
5p - 2q = 5

so

5p - (-3p) = 5 .......using (4)
5p + 3p = 5
8p = 5

so (dividing both sides by 8)

p=5/8

Now, I can put this value of p into equation (4) as follows:

2q = -3p ..............(4)
2q = -3(5/8)
2q = -15/8

so (dividing both sides by 2)

q = -15/16

So I've found possible values for both p and q.

Checking with the original equations,

3p + 4q = 2q ...........(1)
3(5/8) + 4(-15/16) = 2(-15/16)
15/8 - 15/4 = -15/8

I don't like fractions, so I'll multiply both sides by 8, giving:

15 - 30 = -15

which is true so equation (1) is OK.


5p - 2q = 5 ...........(2)
5(5/8) - 2(-15/16) = 5
25/8 + 15/8 = 5
40/8 = 5

which is true so equation (2) is also OK.

This means that we have found the right solution to your problem.

Other simultaneous equations of this type can also be solved using this method:

First, find one of the unknowns (say q) in terms of the other (p), using one of the equations (say 1). Then, substitute this into the other equation (2). This gives an equation with only q in it which you can solve and find q. Then you can use this value to find p.

I hope that you understand everything I've written here. If not, please write back and I'll try to help you some more.

The best way to learn this method is to write out the solution to this question yourself (check my algebra!) and then do a few more examples. If you would like, I would be happy to send you some, but your teacher probably also has some examples.

I hope this all makes sense.

Peter

By Laura-Anne Robinson (P1563) on Monday, December 6, 1999 - 07:27 pm:

Hi Peter (Pmpfr2)
Thanks for writing back so quickly. I have read through what you wrote and i find it easier to work them out now.
You have helped loads,
Thanks again
Laura-Anne