Let V = the value of xy

V = xy

Since x + y = 19, 
          y = 19-x

V = x(19-x)

V = 19x - x²

That's a quadratic equation like y = ax²+bx+c,
because we can write it this way:

V = -x² + 19x + 0

Then you can use the vertex formula to find
the maximum (peak) value, since it's one of
those upside-down U curves, which has its
maximum at the top (the vertex), which you
can tell because the coefficient of x² is
negative.

[If you're in calculus, you just take the 
derivative dV/dx and set it equal to 0.  You get 
the same maximum (vertex) value the algebra 
way or the calculus way).

You finish.  Or you can ask me to help you
finish it, by telling me in the thank-you note
form below.  Then I will get back to you by email.
No charge.  I'm a old retired prof.  No charge.
I do high school and college math for fun, like 
other retired people do crossword puzzles for fun.
I prefer working math problems and explaining them 
to kids for fun. 

Edwin