@zareen said in MTH603 Assignment 1 Solution and Discussion:

Question #2: Solve the system of linear equations with the help of Gaussian elimination method.

2x + y + z = 9;3x −2y + 4z = 9;x +y-2z = 3

System of Linear Equations entered :

[1] 2x + y + z = 9

[2] 3x - 2y + 4z = 9

[3] x + y - 2z = 3

Solve by Substitution :

// Solve equation [3] for the variable y

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

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

[1] 2x + (-x +2z+3) + z = 9

[1] x + 3z = 6

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

[2] 3x - 2•(-x +2z+3) + 4z = 9

[2] 5x = 15

// Solve equation [2] for the variable x

[2] 5x = 15

[2] x = 3

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

[1] (3) + 3z = 6

[1] 3z = 3

// Solve equation [1] for the variable z

[1] 3z = 3

[1] z = 1

// By now we know this much :

x = 3

y = -x+2z+3

z = 1

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

y = -(3)+2(1)+3 = 2

Solution :

{x,y,z} = {3,2,1}