Question

Solve the system of equation In three variables
2x+y-2z=-1 (1)
3x-3y-z=5 (2)
x-2y+3z=6 (3)

Answer 1

Answer:

Solve equation [3] for the variable x

[3] x = 2y - 3z + 6

// Plug this in for variable x in equation [1]

[1] 2•(2y-3z+6) + y - 2z = -1

[1] 5y - 8z = -13

// Plug this in for variable x in equation [2]

[2] 3•(2y-3z+6) - 3y - z = 5

[2] 3y - 10z = -13

// Solve equation [2] for the variable y

[2] 3y = 10z - 13

[2] y = 10z/3 - 13/3

// Plug this in for variable y in equation [1]

[1] 5•(10z/3-13/3) - 8z = -13

[1] 26z/3 = 26/3

[1] 26z = 26

// Solve equation [1] for the variable z

[1] 26z = 26

[1] z = 1

// By now we know this much :

x = 2y-3z+6

y = 10z/3-13/3

z = 1

// Use the z value to solve for y

y = (10/3)(1)-13/3 = -1

// Use the y and z values to solve for x

x = 2(-1)-3(1)+6 = 1

Answer 2

Solve the system of equation In three variables

2x+y-2z=-1 (1)

3x-3y-z=5 (2)

x-2y+3z=6 (3)

X=1. Y=-1 Z=1