Find solutions of system of equalities that satisfy y z
System:
x + y + z = 12
x + yz = 19

Question

Find solutions of system of equalities that satisfy y > z
System:
x + y + z = 12
x + yz = 19

mathmate · Answer

Hints:
1. Solve for the limiting case where y=z, i.e. solve the system
    x+y+y=12; x+y*y = 19
    The solution consists of two values of y={y1,y2}, which are the two limiting values.
    I.e. either   $y1\le y \le y2$   , or, $(-\infty,y] \cup [y\le +\infty)$ 
    Check the domain that is valid, and call this D(y).
2. Solve original system for x and z in terms of y, i.e. x(y), and z(y).
    The solution is therefore x(y), and z(y) with y $\in$ D(y).