Three solutions of an equation in x, y, and z are given. Find the equation. Ax+By+Cz=12; (1,3/4,3), (4/3,1,2), and (2,1,1)

Question

Please show steps.

Answer 1

We will use the points to form a system of equations.

 

First point:  (1, 3/4, 3)

 

A + (3/4)B + 3C = 12

4A + 3B + 12C = 48                 eq1

 

 

Second point:   (4/3, 1, 2)

 

(4/3)A + B + 2C = 12

4A + 3B + 6C = 36                    eq2

 

 

Third point:    (2, 1, 1)

 

2A + B + C = 12                        eq3

 

 

The 3 bolded equations are your system of equations.  Your job is to use substitution/elimination method to solve the system for A, B, and C.