system of equations

Question

Use any method to show how to find the solution set of the following system. State the method used.

 

-x+y-z=-14

2x-y+z=21

3x+2y+z=19

Answer 1

Using Cramer's rule, the principal determinant has rows

 

(-1  1  -1)

(2  -1   1)

(3   2   1)

 

D = -3

 

The determinant of the constants in the x column has rows

 

(-14   1  -1)

( 21  -1   1)

( 19   2   1)

 

D_x = -21

 

x = D_x/D = -21/-3 = 7

 

The determinant of the constants in the y column has rows

 

(-1  -14  -1)

(2     21   1)

(3     19   1)

 

D_y = 9

 

y = D_y/D = 9/-3 = -3

 

The determinant of the constants in the z column has rows

(-1   1  -14)
(2   -1   21)
(3    2   19)

D_z = -12

z = D_z/D = -12/-3 = 4

 

Test the solution.