7x + 3y = p

4x - 6y = p2



Multiply the first equation by 2 to eliminate the terms in y:

`

14x + 6y = 2p

`

 4x - 6y = p2

`

Add the two equations vertically term by term

`

18x      = 2p - p2

`

Divide both sides by 18,

`

x = (2p - p2)/18

`

or if you like you can factor p

 out of the numeration

`

x = p(2-p)/18

`

Ordinarily we would substitute this in one of the original equations 

to find y.  However, when the value is troublesome to substitute in, it 

is much easier to start over and eliminate the other variable, x.

`

7x + 3y = p

`

4x - 6y = p2

`

We can eliminate the x terms in the first by multiplying the 

first equation by 4 and the second equation by -7

`

 28x + 12y = -7p

`

-28x + 42y = 7p2

Adding these gives

       54y = -7p+7p2

         y = (-7p+7p2)/54

`

and you may factor out -7p

 and end up with

`

y = -7p(1-p)/54



Edwin 

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