Question 20126
<pre><font face = "courier new" size 3>7x + 3y = p
4x - 6y = p<sup>2</sup>

Multiply the first equation by 2 to eliminate the terms in y:
`
14x + 6y = 2<font face = "symbol">p</font>
`
 4x - 6y = <font face = "symbol">p</font><sup>2</sup>
`
Add the two equations vertically term by term
`
18x      = 2<font face = "symbol">p</font> - <font face = "symbol">p</font><sup>2</sup>
`
Divide both sides by 18,
`
x = (2<font face = "symbol">p</font> - <font face = "symbol">p</font><sup>2</sup>)/18
`
or if you like you can factor <font face = "symbol">p</font>
 out of the numeration
`
x = <font face = "symbol">p</font>(2-<font face = "symbol">p</font>)/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 = <font face = "symbol">p</font>
`
4x - 6y = <font face = "symbol">p</font><sup>2</sup>
`
We can eliminate the x terms in the first by multiplying the 
first equation by 4 and the second equation by -7
`
 28x + 12y = -7<font face = "symbol">p</font>
`
-28x + 42y = 7<font face = "symbol">p</font><sup>2</sup>
Adding these gives
       54y = -7<font face = "symbol">p</font>+7<font face= "symbol">p</font><sup>2</sup>
         y = (-7<font face = "symbol">p</font>+7<font face = "symbol">p</font><sup>2</sup>)/54
`
and you may factor out -7<font face = "symbol">p</font>
 and end up with
`
y = -7<font face = "symbol">p</font>(1-<font face = "symbol">p</font>)/54

Edwin