Nonlinear Equations with Four Variables: Solving for All Solutions

[dirk_mec1]

Homework Statement

Find all solutions of:

a + c = 5
b + d + ac = 5
ad+ bc = 5
bd = -6

Homework Equations

The Attempt at a Solution

I tried subsitution and end up with a cubic equations. I am pretty sure it can be done easier.

 

[phyzguy]

Why do you think it can be done more simply? I got a 6th order equation. Mathematica came up with 6 solutions, two real and 4 complex. Try showing us your work.

 

[dirk_mec1]

Because this is written in a high school book. So there must be something we are overlooking.