@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}