Question

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

Answer 1

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).